
SUBFILE: MOFI4.OLD @14:26 2-APR-1981 <005> (1026)    

yes
| ?- input(mofi4).

Problem from file : mofi4.prb

Radius of Gyration of a parallelogram

 Let pagrm be a new parallelogram
 Let top be a new line
 Let bot be a new line
 Let left be a new line
 Let right be a new line
 Note: b (of type length) was used in a perp_dist definition (3)
 Note: [90,0] (of type angle) was used in a perp_dist definition (4)
 Note: -b (of type length) was used in a perp_dist definition (3)
 Note: -a (of type length) was used in a perp_dist definition (3)
 Note: [alpha-90,0] (of type angle) was used in a perp_dist definition (4)
 Note: a (of type length) was used in a perp_dist definition (3)
 Note: m (of type mass) was used in a mass definition (2)
 Let axis(rr) be a new line
 Let typical_point4 be a new typical_point
 Note: [alpha,0] (of type angle) was used in a incline definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi4 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown   ( continue after error )

Attempting to solve for [k] in terms of [a,b,alpha,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(pagrm,axis(rr)))
 Let line1 be a new line
 Let point1 be a new point
 Let point2 be a new point
 Let origin2 be a new point

 line1 is new fibre defined by 
    isa(line,line1)
    line_sys(line1,point1,point2)
    isa(point,point1)
    isa(point,point2)
    isa(point,origin2)
    on(origin2,line1)
    separation(origin2,point1,-a-y1*cos(alpha),[0,0])
    separation(origin2,point2,a+y1*cos(alpha),[0,0])


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(pagrm,axis(rr)))
 Let mass1 be the mass of line1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*((a*-1+y1*cos(alpha)*-1+a+y1*cos(alpha)+a+y1*cos(alpha))*sin(alpha-0)/sqrt(3))^2,-b,b,rr)
 formed by applying : strategy(moment_of_inertia,situation(pagrm,axis(rr)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,b,alpha,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(line1))
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(line1))
 Let mass_per_area1 be the mass_per_area of pagrm.
 Note: mass_per_area1 (of type mass) was used in a mass_per_area definition (2)

 Equation-2 : mass1=(a*-1+y1*cos(alpha)*-1+a+y1*cos(alpha)+a+y1*cos(alpha)-(a*-1+y1*cos(alpha)*-1+a+y1*cos(alpha)+a+y1*cos(alpha)+a*-1+y1*cos(alpha)*-1+a*-1+y1*cos(alpha)*-1))*(d(y1)*mass_per_area1)
 formed by applying : strategy(mass_per_length,situation(line1))

 This equation solves for mass1 but introduces [mass_per_area1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_area1]
		   given [mass1,k,a,b,alpha,m]

I am now trying to solve for mass_per_area1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(pagrm))

 Equation-3 : m=(b-(-b))*(a/sin(alpha)-(-a)/sin(alpha))*mass_per_area1
 formed by applying : strategy(mass_per_area,situation(pagrm))

 This equation solves for mass_per_area1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_area1,mass1,k,a,b,alpha,m]


Equations extracted : 
    m*k^2=integrate(mass1*((a*-1+y1*cos(alpha)*-1+a+y1*cos(alpha)+a+y1*cos(alpha))*sin(alpha-0)/sqrt(3))^2,-b,b,rr)
    mass1=(a*-1+y1*cos(alpha)*-1+a+y1*cos(alpha)+a+y1*cos(alpha)-(a*-1+y1*cos(alpha)*-1+a+y1*cos(alpha)+a+y1*cos(alpha)+a*-1+y1*cos(alpha)*-1+a*-1+y1*cos(alpha)*-1))*(d(y1)*mass_per_area1)
    m=(b-(-b))*(a/sin(alpha)-(-a)/sin(alpha))*mass_per_area1


yes
| ?- core     90112  (60928 lo-seg + 29184 hi-seg)
heap     55808 =  54138 in use +   1670 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.69 sec. for 2 GCs gaining 38184 words
    0.98 sec. for 27 local shifts and 35 trail shifts
   11.96 sec. runtime




\\\\\



SUBFILE: MOFI1.SOL @16:29 1-APR-1981 <005> (586)     

yes
| ?- restore(save).

yes
| ?- input(mofi1).

Problem from file : mofi1.prb

Radius of Gyration of a line

 Let l1 be a new line
 Let l be a new point
 Let r be a new point
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi1 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown -- [a]
   ( continue after error )

Attempting to solve for [k] in terms of [a,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(l1,axis(y)))
 Let point1 be a new point

 point1 is new fibre defined by 
    isa(point,point1)
    separation(origin,point1,r1,[0,0])


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(l1,axis(y)))
 Let mass_per_length1 be the mass_per_length of l1.
 Note: mass_per_length1 (of type mass) was used in a mass_per_length definition (2)

 Equation-1 : m*k^2=integrate(d(r1)*mass_per_length1*(a*-1+a+a+r1+a+a*-1+a*-1)^2,a*-1+a+a+a*-1+a*-1,a*-1+a+a,y)
 formed by applying : strategy(moment_of_inertia,situation(l1,axis(y)))

 This equation solves for k but introduces [mass_per_length1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_length1]
		   given [k,a,m]

I am now trying to solve for mass_per_length1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(l1))

 Equation-2 : m=(a*-1+a+a+r1+a+a*-1+a*-1+r1*-1+a*-1+a+a-(a*-1+a+a+r1+a+a*-1+a*-1+a*-1+a*-1+r1*-1+a*-1+a+a))*mass_per_length1
 formed by applying : strategy(mass_per_length,situation(l1))

 This equation solves for mass_per_length1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_length1,k,a,m]


Equations extracted : 
    m*k^2=integrate(d(r1)*mass_per_length1*(a*-1+a+a+r1+a+a*-1+a*-1)^2,a*-1+a+a+a*-1+a*-1,a*-1+a+a,y)
    m=(a*-1+a+a+r1+a+a*-1+a*-1+r1*-1+a*-1+a+a-(a*-1+a+a+r1+a+a*-1+a*-1+a*-1+a*-1+r1*-1+a*-1+a+a))*mass_per_length1


yes
| ?- core     83456  (54272 lo-seg + 29184 hi-seg)
heap     49152 =  48243 in use +    909 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.05 sec. for 2 GCs gaining 993 words
    0.51 sec. for 26 local shifts and 43 trail shifts
   11.01 sec. runtime




\\\\\


SUBFILE: MOFI2.SOL @10:35 2-APR-1981 <005> (897)     

| ?- input(mofi2).

Problem from file : mofi2.prb

Radius of Gyration of a rectangle

 Let rect be a new rectangle
 Let top be a new line
 Let bot be a new line
 Let left be a new line
 Let right be a new line
 Note: b (of type length) was used in a perp_dist definition (3)
 Note: [90,0] (of type angle) was used in a perp_dist definition (4)
 Note: -b (of type length) was used in a perp_dist definition (3)
 Note: -a (of type length) was used in a perp_dist definition (3)
 Note: [0,0] (of type angle) was used in a perp_dist definition (4)
 Note: a (of type length) was used in a perp_dist definition (3)
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi2 problem read into data base. 


yes
| ?- go.

Attempting to solve for [k] in terms of [a,b,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(rect,axis(y)))

** ERROR nfrec3   ( continue after error )
 Let line1 be a new line
 Let point1 be a new point
 Let point2 be a new point
 Let typ_pt1 be a new point

 line1 is new fibre defined by 
    isa(line,line1)
    line_sys(line1,point1,point2)
    isa(point,point1)
    isa(point,point2)
    isa(point,typ_pt1)
    on(typ_pt1,line1)
    separation(typ_pt1,point1,-a,[0,0])
    separation(typ_pt1,point2,a,[0,0])


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(rect,axis(y)))
 Let mass1 be the mass of line1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*((a*-1+a+a)/sqrt(3))^2,-b,b,y)
 formed by applying : strategy(moment_of_inertia,situation(rect,axis(y)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,b,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(line1))
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(line1))
 Let mass_per_area1 be the mass_per_area of rect.
 Note: mass_per_area1 (of type mass) was used in a mass_per_area definition (2)

 Equation-2 : mass1=(a*-1+a+a-(a*-1+a+a+a*-1+a*-1))*(d(y1)*mass_per_area1)
 formed by applying : strategy(mass_per_length,situation(line1))

 This equation solves for mass1 but introduces [mass_per_area1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_area1]
		   given [mass1,k,a,b,m]

I am now trying to solve for mass_per_area1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(rect))

 Equation-3 : m=(b-(-b))*(a-(-a))*mass_per_area1
 formed by applying : strategy(mass_per_area,situation(rect))

 This equation solves for mass_per_area1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_area1,mass1,k,a,b,m]


Equations extracted : 
    m*k^2=integrate(mass1*((a*-1+a+a)/sqrt(3))^2,-b,b,y)
    mass1=(a*-1+a+a-(a*-1+a+a+a*-1+a*-1))*(d(y1)*mass_per_area1)
    m=(b-(-b))*(a-(-a))*mass_per_area1


yes
| ?- core     87552  (58368 lo-seg + 29184 hi-seg)
heap     53248 =  51256 in use +   1992 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.03 sec. for 1 GCs gaining 556 words
    0.24 sec. for 11 local shifts and 17 trail shifts
    4.52 sec. runtime




\\\\\


SUBFILE: MOFI3.SOL @11:46 7-APR-1981 <005> (654)     
| ?- input(mofi3).

Problem from file : mofi3.prb

Radius of Gyration of an inclined line

 Let l1 be a new line
 Let l be a new point
 Let r be a new point
 Note: -a (of type length) was used in a separation definition (3)
 Note: [0,0] (of type angle) was used in a separation definition (4)
 Note: a (of type length) was used in a separation definition (3)
 Note: m (of type mass) was used in a mass definition (2)
 Let axis(rr) be a new line
 Let typical_point4 be a new typical_point
 Note: [alpha,0] (of type angle) was used in a incline definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi3 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown: alpha
   ( continue after error )

Attempting to solve for [k] in terms of [a,alpha,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(l1,axis(rr)))
 Let point1 be a new point
 Note: r1 (of type length) was used in a separation definition (3)

 point1 is new fibre defined by 
    isa(point,point1)
    separation(origin,point1,r1,[0,0])

 Note: x1/cos(alpha) (of type length) was used in a separation definition (3)
 Note: [alpha,0] (of type angle) was used in a separation definition (4)

No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(l1,axis(rr)))
 Let mass_per_length1 be the mass_per_length of l1.
 Note: mass_per_length1 (of type mass) was used in a mass_per_length definition (2)

 Equation-1 : m*k^2=integrate(d(r1)*mass_per_length1*(r1*sin(alpha-0))^2,-a,a,r1)
 formed by applying : strategy(moment_of_inertia,situation(l1,axis(rr)))

 This equation solves for k but introduces [mass_per_length1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_length1]
		   given [k,a,alpha,m]

I am now trying to solve for mass_per_length1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(l1))

 Equation-2 : m=(a-(-a))*mass_per_length1
 formed by applying : strategy(mass_per_length,situation(l1))

 This equation solves for mass_per_length1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_length1,k,a,alpha,m]


Equations extracted : 
    m*k^2=integrate(d(r1)*mass_per_length1*(r1*sin(alpha-0))^2,-a,a,r1)
    m=(a-(-a))*mass_per_length1


yes
| ?- core     93184  (64000 lo-seg + 29184 hi-seg)
heap     58880 =  56798 in use +   2082 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.02 sec. for 1 GCs gaining 353 words
    0.14 sec. for 12 local shifts and 18 trail shifts
    7.89 sec. runtime




\\\\\


SUBFILE: MOFI4.SOL @16:55 6-APR-1981 <005> (1174)    

yes
| ?- input(mofi4).

Problem from file : mofi4.prb

Radius of Gyration of a parallelogram

 Let pagrm be a new parallelogram
 Let top be a new line
 Let bot be a new line
 Let left be a new line
 Let right be a new line
 Note: b (of type length) was used in a perp_dist definition (3)
 Note: [90,0] (of type angle) was used in a perp_dist definition (4)
 Note: -b (of type length) was used in a perp_dist definition (3)
 Note: -a (of type length) was used in a perp_dist definition (3)
 Note: [alpha-90,0] (of type angle) was used in a perp_dist definition (4)
 Note: a (of type length) was used in a perp_dist definition (3)
 Note: m (of type mass) was used in a mass definition (2)
 Let axis(rr) be a new line
 Let typical_point4 be a new typical_point
 Note: [alpha,0] (of type angle) was used in a incline definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi4 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown: alpha
   ( continue after error )

Attempting to solve for [k] in terms of [a,b,alpha,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(pagrm,axis(rr)))
 Note: x1/cos(alpha) (of type length) was used in a separation definition (3)
 Note: [alpha,0] (of type angle) was used in a separation definition (4)
 Note: y1/sin(alpha) (of type length) was used in a separation definition (3)
 Let line1 be a new line
 Let point1 be a new point
 Let point2 be a new point
 Let origin2 be a new point
 Note: a*sin(alpha)^-1*-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1 (of type length) was used in a separation definition (3)
 Note: [0,0] (of type angle) was used in a separation definition (4)
 Note: a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1 (of type length) was used in a separation definition (3)

 line1 is new fibre defined by 
    isa(line,line1)
    line_sys(line1,point1,point2)
    isa(point,point1)
    isa(point,point2)
    isa(point,origin2)
    on(origin2,line1)
    separation(origin2,point1,a*sin(alpha)^-1*-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1,[0,0])
    separation(origin2,point2,a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1,[0,0])


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(pagrm,axis(rr)))
 Let mass1 be the mass of line1.
 Note: mass1 (of type mass) was used in a mass definition (2)
 Let -(a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1) be the separation of origin2 in direction [0,0] at point1.
 Note: -(a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1) (of type length) was used in a separation definition (3)

 Equation-1 : m*k^2=integrate(mass1*((a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1)*sin(alpha-0)/sqrt(3))^2,-b,b,y1)
 formed by applying : strategy(moment_of_inertia,situation(pagrm,axis(rr)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,b,alpha,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(line1))
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(line1))
 Let mass_per_area1 be the mass_per_area of pagrm.
 Note: mass_per_area1 (of type mass) was used in a mass_per_area definition (2)

 Equation-2 : mass1=(a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1- -(a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1))*(d(y1)*mass_per_area1)
 formed by applying : strategy(mass_per_length,situation(line1))

 This equation solves for mass1 but introduces [mass_per_area1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_area1]
		   given [mass1,k,a,b,alpha,m]

I am now trying to solve for mass_per_area1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(pagrm))

 Equation-3 : m=(b-(-b))*(a/sin(alpha)-(-a)/sin(alpha))*mass_per_area1
 formed by applying : strategy(mass_per_area,situation(pagrm))

 This equation solves for mass_per_area1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_area1,mass1,k,a,b,alpha,m]


Equations extracted : 
    m*k^2=integrate(mass1*((a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1)*sin(alpha-0)/sqrt(3))^2,-b,b,y1)
    mass1=(a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1- -(a*sin(alpha)^-1+y1*tan(alpha)^-1+tan(alpha)*y1*-1))*(d(y1)*mass_per_area1)
    m=(b-(-b))*(a/sin(alpha)-(-a)/sin(alpha))*mass_per_area1


yes
| ?- core     93696  (64512 lo-seg + 29184 hi-seg)
heap     59392 =  57587 in use +   1805 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.02 sec. for 1 GCs gaining 353 words
    0.33 sec. for 16 local shifts and 28 trail shifts
   10.90 sec. runtime




\\\\\


SUBFILE: MOFI5.SOL @16:37 1-APR-1981 <005> (570)     

yes
| ?- input(mofi5).

Problem from file : mofi5.prb

Radius of Gyration of a ring

 Let ring1 be a new ring
 Note: a (of type length) was used in a radius definition (2)
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi5 problem read into data base. 


yes
| ?- go.

Attempting to solve for [k] in terms of [a,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(ring1,axis(z)))
 Let point1 be a new point

 point1 is new fibre defined by 
    isa(point,point1)
    separation(origin,point1,a,[theta1,0])


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(ring1,axis(z)))
 Let mass_per_length1 be the mass_per_length of ring1.
 Note: mass_per_length1 (of type mass) was used in a mass_per_length definition (2)

 Equation-1 : m*k^2=integrate(d(theta1)*mass_per_length1*((a^2)^number(+,[1],[2]))^2,0,2*pi,z)
 formed by applying : strategy(moment_of_inertia,situation(ring1,axis(z)))

 This equation solves for k but introduces [mass_per_length1,+].

[ Unknowns allowed ]   Do you accept this equation ? yes.

** ERROR Type unknown -- [+]
   ( continue after error )

 So now I must solve for [mass_per_length1,+]
		   given [k,a,m]

I am now trying to solve for mass_per_length1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))

 Equation-2 : m=2*pi*a*mass_per_length1
 formed by applying : strategy(mass_per_length,situation(ring1))

 This equation solves for mass_per_length1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for [+]
		   given [mass_per_length1,k,a,m]

I am now trying to solve for + without introducing any unknowns.

No luck - I will now accept unknowns in solving for +.

I am unable to solve for +.

I will go back to solve for k again

 Equation-1 rejected.


I am unable to solve for k.

no
| ?- core     83456  (54272 lo-seg + 29184 hi-seg)
heap     49152 =  48078 in use +   1074 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.01 sec. for 1 GCs gaining 353 words
    0.22 sec. for 18 local shifts and 21 trail shifts
    4.90 sec. runtime




\\\\\


SUBFILE: MOFI6.SOL @16:43 1-APR-1981 <005> (763)     

yes
| ?- input(mofi6).

Problem from file : mofi6.prb

Radius of Gyration of a Disc

 Let disc1 be a new disc
 Note: a (of type length) was used in a radius definition (2)
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi6 problem read into data base. 


yes
| ?- go.

Attempting to solve for [k] in terms of [a,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(disc1,axis(z)))
 Let ring1 be a new ring
 Note: r1 (of type length) was used in a radius definition (2)

 ring1 is new fibre defined by 
    isa(ring,ring1)
    centre(ring1,origin)
    radius(ring1,r1)
    meets(axis(z),ring1,origin)


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(disc1,axis(z)))
 Let mass1 be the mass of ring1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*r1^2,0,a,z)
 formed by applying : strategy(moment_of_inertia,situation(disc1,axis(z)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))
 Let mass_per_area1 be the mass_per_area of disc1.
 Note: mass_per_area1 (of type mass) was used in a mass_per_area definition (2)
 Let line_sys1 be the line_sys of ring1 Let line_sys2 be the line_sys of ring1.

 Equation-2 : mass1=2*pi*r1*(d(r1)*mass_per_area1)
 formed by applying : strategy(mass_per_length,situation(ring1))

 This equation solves for mass1 but introduces [mass_per_area1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_area1]
		   given [mass1,k,a,m]

I am now trying to solve for mass_per_area1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))

 Equation-3 : m=pi*a^2*mass_per_area1
 formed by applying : strategy(mass_per_area,situation(disc1))

 This equation solves for mass_per_area1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_area1,mass1,k,a,m]


Equations extracted : 
    m*k^2=integrate(mass1*r1^2,0,a,z)
    mass1=2*pi*r1*(d(r1)*mass_per_area1)
    m=pi*a^2*mass_per_area1


yes
| ?- core     83456  (54272 lo-seg + 29184 hi-seg)
heap     49152 =  48080 in use +   1072 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.05 sec. for 1 GCs gaining 494 words
    0.12 sec. for 9 local shifts and 14 trail shifts
    3.05 sec. runtime




\\\\\


SUBFILE: MOFI7.SOL @17:5 1-APR-1981 <005> (757)      
| ?- input(mofi7).

Problem from file : mofi7.prb

Radius of Gyration of a sphere

 Let sphere1 be a new sphere
 Note: a (of type length) was used in a radius definition (2)
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi7 problem read into data base. 


yes
| ?- go.

Attempting to solve for [k] in terms of [a,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(sphere1,axis(z)))
 Let disc1 be a new disc
 Note: sqrt(a^2-z1^2) (of type length) was used in a radius definition (2)

 disc1 is new fibre defined by 
    isa(disc,disc1)
    centre(disc1,typ_pt1)
    radius(disc1,sqrt(a^2-z1^2))
    meets(axis(z),disc1,typ_pt1)


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(sphere1,axis(z)))
 Let mass1 be the mass of disc1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*(sqrt(a^2-z1^2)/sqrt(2))^2,-a,a,z)
 formed by applying : strategy(moment_of_inertia,situation(sphere1,axis(z)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))
 (try  mass_per_length)
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))
 Let mass_per_vol1 be the mass_per_vol of sphere1.
 Note: mass_per_vol1 (of type mass) was used in a mass_per_vol definition (2)

 Equation-2 : mass1=pi*sqrt(a^2-z1^2)^2*(d(z1)*mass_per_vol1)
 formed by applying : strategy(mass_per_area,situation(disc1))

 This equation solves for mass1 but introduces [mass_per_vol1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_vol1]
		   given [mass1,k,a,m]

I am now trying to solve for mass_per_vol1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 Trying to apply strategy(mass_per_vol,situation(sphere1))

 Equation-3 : m=4/3*pi*a^3*mass_per_vol1
 formed by applying : strategy(mass_per_vol,situation(sphere1))

 This equation solves for mass_per_vol1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_vol1,mass1,k,a,m]


Equations extracted : 
    m*k^2=integrate(mass1*(sqrt(a^2-z1^2)/sqrt(2))^2,-a,a,z)
    mass1=pi*sqrt(a^2-z1^2)^2*(d(z1)*mass_per_vol1)
    m=4/3*pi*a^3*mass_per_vol1


yes
| ?- core     83968  (54784 lo-seg + 29184 hi-seg)
heap     49664 =  48440 in use +   1224 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.01 sec. for 1 GCs gaining 312 words
    0.17 sec. for 10 local shifts and 15 trail shifts
    3.40 sec. runtime




\\\\\


SUBFILE: MOFI8.SOL @12:13 2-APR-1981 <005> (780)     
| ?- input(mofi8).

Problem from file : mofi8.prb

Radius of Gyration of a shell

 Let shell1 be a new shell
 Note: a (of type length) was used in a radius definition (2)
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi8 problem read into data base. 


yes
| ?- go.

Attempting to solve for [k] in terms of [a,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(shell1,axis(z)))
 Let ring1 be a new ring
 Note: sqrt(a^2-z1^2) (of type length) was used in a radius definition (2)

 ring1 is new fibre defined by 
    isa(ring,ring1)
    centre(ring1,origin1)
    radius(ring1,sqrt(a^2-z1^2))
    meets(axis(z),ring1,origin1)


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(shell1,axis(z)))
 Let mass1 be the mass of ring1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*sqrt(a^2-z1^2)^2,-a,a,z)
 formed by applying : strategy(moment_of_inertia,situation(shell1,axis(z)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))
 Let mass_per_area1 be the mass_per_area of shell1.
 Note: mass_per_area1 (of type mass) was used in a mass_per_area definition (2)
 Let line_sys1 be the line_sys of ring1 Let line_sys2 be the line_sys of ring1.

 Equation-2 : mass1=2*pi*sqrt(a^2-z1^2)*(d(z1)*mass_per_area1)
 formed by applying : strategy(mass_per_length,situation(ring1))

 This equation solves for mass1 but introduces [mass_per_area1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_area1]
		   given [mass1,k,a,m]

I am now trying to solve for mass_per_area1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(shell1))

 Equation-3 : m=4*pi*a^2*mass_per_area1
 formed by applying : strategy(mass_per_area,situation(shell1))

 This equation solves for mass_per_area1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_area1,mass1,k,a,m]


Equations extracted : 
    m*k^2=integrate(mass1*sqrt(a^2-z1^2)^2,-a,a,z)
    mass1=2*pi*sqrt(a^2-z1^2)*(d(z1)*mass_per_area1)
    m=4*pi*a^2*mass_per_area1


yes
| ?- core     87552  (58368 lo-seg + 29184 hi-seg)
heap     53248 =  51358 in use +   1890 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.02 sec. for 1 GCs gaining 353 words
    0.20 sec. for 13 local shifts and 19 trail shifts
    6.07 sec. runtime




\\\\\


SUBFILE: MOFI9.SOL @13:26 2-APR-1981 <005> (753)     

yes
| ?- input(mofi9).

Problem from file : mofi9.prb

Radius of Gyration of a cylinder

 Let cylinder1 be a new cylinder
 Note: a (of type length) was used in a radius definition (2)

** ERROR reckind   ( continue after error )
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi9 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown   ( continue after error )

Attempting to solve for [k] in terms of [a,h,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(cylinder1,axis(z)))
 Let disc1 be a new disc

 disc1 is new fibre defined by 
    isa(disc,disc1)
    centre(disc1,origin1)
    radius(disc1,a)
    meets(axis(z),disc1,origin1)


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(cylinder1,axis(z)))
 Let mass1 be the mass of disc1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*(a/sqrt(2))^2,0,h,z)
 formed by applying : strategy(moment_of_inertia,situation(cylinder1,axis(z)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,h,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))
 (try  mass_per_length)
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))
 Let mass_per_vol1 be the mass_per_vol of cylinder1.
 Note: mass_per_vol1 (of type mass) was used in a mass_per_vol definition (2)

 Equation-2 : mass1=pi*a^2*(d(z1)*mass_per_vol1)
 formed by applying : strategy(mass_per_area,situation(disc1))

 This equation solves for mass1 but introduces [mass_per_vol1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_vol1]
		   given [mass1,k,a,h,m]

I am now trying to solve for mass_per_vol1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 Trying to apply strategy(mass_per_vol,situation(cylinder1))

 Equation-3 : m=pi*a^2*h*mass_per_vol1
 formed by applying : strategy(mass_per_vol,situation(cylinder1))

 This equation solves for mass_per_vol1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_vol1,mass1,k,a,h,m]


Equations extracted : 
    m*k^2=integrate(mass1*(a/sqrt(2))^2,0,h,z)
    mass1=pi*a^2*(d(z1)*mass_per_vol1)
    m=pi*a^2*h*mass_per_vol1


yes
| ?- core     87552  (58368 lo-seg + 29184 hi-seg)
heap     53248 =  51312 in use +   1936 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.04 sec. for 1 GCs gaining 523 words
    0.18 sec. for 8 local shifts and 14 trail shifts
    3.28 sec. runtime




\\\\\


SUBFILE: MOFI10.SOL @13:28 2-APR-1981 <005> (788)    
Mecho Problem Solver
Prolog-10  version 3.2

| ?- restore(save).

yes
| ?- input(mofi10).

Problem from file : mofi10.prb

Radius of Gyration of a cone

 Let cone1 be a new cone
 Note: a (of type length) was used in a radius definition (2)

** ERROR reckind   ( continue after error )
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi10 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown   ( continue after error )

Attempting to solve for [k] in terms of [a,h,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(cone1,axis(z)))
 Let disc1 be a new disc
 Note: a*(h-z1)/h (of type length) was used in a radius definition (2)

 disc1 is new fibre defined by 
    isa(disc,disc1)
    centre(disc1,origin1)
    radius(disc1,a*(h-z1)/h)
    meets(axis(z),disc1,origin1)


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(cone1,axis(z)))
 Let mass1 be the mass of disc1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*(a*(h-z1)/h/sqrt(2))^2,0,h,z)
 formed by applying : strategy(moment_of_inertia,situation(cone1,axis(z)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,h,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))
 (try  mass_per_length)
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(disc1))
 Let mass_per_vol1 be the mass_per_vol of cone1.
 Note: mass_per_vol1 (of type mass) was used in a mass_per_vol definition (2)

 Equation-2 : mass1=pi*(a*(h-z1)/h)^2*(d(z1)*mass_per_vol1)
 formed by applying : strategy(mass_per_area,situation(disc1))

 This equation solves for mass1 but introduces [mass_per_vol1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_vol1]
		   given [mass1,k,a,h,m]

I am now trying to solve for mass_per_vol1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 Trying to apply strategy(mass_per_vol,situation(cone1))

 Equation-3 : m=1/3*pi*a^2*h*mass_per_vol1
 formed by applying : strategy(mass_per_vol,situation(cone1))

 This equation solves for mass_per_vol1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_vol1,mass1,k,a,h,m]


Equations extracted : 
    m*k^2=integrate(mass1*(a*(h-z1)/h/sqrt(2))^2,0,h,z)
    mass1=pi*(a*(h-z1)/h)^2*(d(z1)*mass_per_vol1)
    m=1/3*pi*a^2*h*mass_per_vol1


yes
| ?- core     87552  (58368 lo-seg + 29184 hi-seg)
heap     53248 =  51370 in use +   1878 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.05 sec. for 1 GCs gaining 523 words
    0.16 sec. for 9 local shifts and 15 trail shifts
    3.37 sec. runtime




\\\\\


SUBFILE: MOFI11.SOL @15:42 3-APR-1981 <005> (792)    
| ?- input(mofi11).

Problem from file : mofi11.prb

Radius of Gyration of a tube

 Let tube1 be a new tube
 Note: a (of type length) was used in a radius definition (2)

** ERROR Cannot record kind for height(tube1,h)
   ( continue after error )
 Note: m (of type mass) was used in a mass definition (2)
 Note: k (of type rofg) was used in a rad_of_gyr definition (3)

mofi11 problem read into data base. 


yes
| ?- go.

** ERROR Type unknown: h
   ( continue after error )

Attempting to solve for [k] in terms of [a,h,m]


I am now trying to solve for k without introducing any unknowns.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(tube1,axis(z)))
  origin and origin1 are seperated by [z1,0,90] during always.
 Let ring1 be a new ring

 ring1 is new fibre defined by 
    isa(ring,ring1)
    centre(ring1,origin1)
    radius(ring1,a)
    meets(axis(z),ring1,origin1)


No luck - I will now accept unknowns in solving for k.

 Applicable formulae : [parallel_axes,moment_of_inertia]
 (try  parallel_axes)
 (try  moment_of_inertia)
 Trying to apply strategy(moment_of_inertia,situation(tube1,axis(z)))
 Let mass1 be the mass of ring1.
 Note: mass1 (of type mass) was used in a mass definition (2)

 Equation-1 : m*k^2=integrate(mass1*a^2,0,h,z1)
 formed by applying : strategy(moment_of_inertia,situation(tube1,axis(z)))

 This equation solves for k but introduces [mass1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass1]
		   given [k,a,h,m]

I am now trying to solve for mass1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))
 (try  resolve)

No luck - I will now accept unknowns in solving for mass1.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 (try  mass_per_length)
 Trying to apply strategy(mass_per_length,situation(ring1))
 Let mass_per_area1 be the mass_per_area of tube1.
 Note: mass_per_area1 (of type mass) was used in a mass_per_area definition (2)
 Let line_sys1 be the line_sys of ring1 Let line_sys2 be the line_sys of ring1.

 Equation-2 : mass1=2*pi*a*(d(z1)*mass_per_area1)
 formed by applying : strategy(mass_per_length,situation(ring1))

 This equation solves for mass1 but introduces [mass_per_area1].

[ Unknowns allowed ]   Do you accept this equation ? yes.

 So now I must solve for [mass_per_area1]
		   given [mass1,k,a,h,m]

I am now trying to solve for mass_per_area1 without introducing any unknowns.

 Applicable formulae : [moment_of_inertia,mass_per_vol,mass_per_area,mass_per_length,resolve]
 (try  moment_of_inertia)
 (try  mass_per_vol)
 (try  mass_per_area)
 Trying to apply strategy(mass_per_area,situation(tube1))

 Equation-3 : m=2*pi*a*h*mass_per_area1
 formed by applying : strategy(mass_per_area,situation(tube1))

 This equation solves for mass_per_area1.

[ No unknowns ]   Do you accept this equation ? yes.

 So now I must solve for []
		   given [mass_per_area1,mass1,k,a,h,m]


Equations extracted : 
    m*k^2=integrate(mass1*a^2,0,h,z1)
    mass1=2*pi*a*(d(z1)*mass_per_area1)
    m=2*pi*a*h*mass_per_area1


yes
| ?- core     88064  (58880 lo-seg + 29184 hi-seg)
heap     53760 =  51520 in use +   2240 free
global    1187 =     16 in use +   1171 free
local     1024 =     16 in use +   1008 free
trail      511 =      0 in use +    511 free
    0.01 sec. for 1 GCs gaining 353 words
    0.19 sec. for 12 local shifts and 20 trail shifts
    6.13 sec. runtime




\\\\\


