Ronan

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6 years, 253 days
East Grinstead, United Kingdom

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These are questions asked by Ronan

I am working with Euler's eqns. of motion. So want to animate the solution. I could do a simple set of spheres along the x, y, z axes  that represent the body or use an imported STL file.  Looking for some guidance on how to approech this. I can import an STL ok. How do I give it an xyz set of axes and then rotate/move these in an inertial frame? I have the equations and solutions already. A reasonable example would be adding an STL of a pendulum to http://www.mapleprimes.com/questions/220957-Non-Simple-Harmonic-Pendulum-Motion#answer235955  to Preben's animation response to a recent post  I placed.

 

The first half of this work sheet deals with SHM of pendulum. In the second half of the work sheet I attempt to solve for the general case of a swinging pendulum. Maple introduces a place holder (correct me if I have used the incorrect termonology) " __a" which I do not understand. What variable(s) should I replace it with and is there an automatic way of doing so?
 

restart

NULL

``

``

Simple*Harmonic*Motion*of*a*Pendulum

NULL

Eq1 := diff(Theta(t), t, t) = -omega^2*Theta(t)

diff(diff(Theta(t), t), t) = -omega^2*Theta(t)

(1)

ics := Theta(0) = 0, (D(Theta))(0) = Vmax

Theta(0) = 0, (D(Theta))(0) = Vmax

(2)

SHM := dsolve({Eq1, ics})

Theta(t) = Vmax*sin(omega*t)/omega

(3)

diffSHM := diff(SHM, t)

diff(Theta(t), t) = Vmax*cos(omega*t)

(4)

convert(diffSHM, D)

(D(Theta))(t) = Vmax*cos(omega*t)

(5)

eval[recurse](%, {t = 0, (D(Theta))(0) = Vmax})

Vmax = Vmax

(6)

solve(%, {_C1})

{_C1 = _C1}

(7)

assign(%); _C1

_C1

(8)

``

SHM

Theta(t) = Vmax*sin(omega*t)/omega

(9)

``

(General*Equation*of*Motion*of)*a*Pendulum

restart

diff(Theta(t), t, t) = -omega^2*sin(Theta(t))

diff(diff(Theta(t), t), t) = -omega^2*sin(Theta(t))

(10)

ics := Theta(0) = 0, (D(Theta))(0) = Vmax

Theta(0) = 0, (D(Theta))(0) = Vmax

(11)

Sol := dsolve(diff(Theta(t), t, t) = -omega^2*sin(Theta(t)))

Intat(1/(2*omega^2*cos(_a)+_C1)^(1/2), _a = Theta(t))-t-_C2 = 0, Intat(-1/(2*omega^2*cos(_a)+_C1)^(1/2), _a = Theta(t))-t-_C2 = 0

(12)

Sol[1]

Intat(1/(2*omega^2*cos(_a)+_C1)^(1/2), _a = Theta(t))-t-_C2 = 0

(13)

_C2 := 0

0

(14)

Sol[1]

Intat(1/(2*omega^2*cos(_a)+_C1)^(1/2), _a = Theta(t))-t = 0

(15)

``

dffSol[1] := diff(Sol[1], t)

(diff(Theta(t), t))/(2*omega^2*cos(Theta(t))+_C1)^(1/2)-1 = 0

(16)

``convert(dffSol[1], D)

(D(Theta))(t)/(2*omega^2*cos(Theta(t))+_C1)^(1/2)-1 = 0

(17)

 

eval[recurse](%, {t = 0, Theta(0) = 0, (D(Theta))(0) = Vmax})

Vmax/(2*omega^2+_C1)^(1/2)-1 = 0

(18)

solve(%, {_C1})

{_C1 = Vmax^2-2*omega^2}

(19)

assign(%); 1; _C1

Vmax^2-2*omega^2

(20)

dffSol[1]

(diff(Theta(t), t))/(2*omega^2*cos(Theta(t))+Vmax^2-2*omega^2)^(1/2)-1 = 0

(21)

``

dsolve(dffSol[1]); 1; SOL1 := int((diff(Theta(t), t))/sqrt(2*omega^2*cos(Theta(t))+Vmax^2-2*omega^2)-1, t = 0 .. Theta(t)) = 0

int((diff(Theta(t), t))/(2*omega^2*cos(Theta(t))+Vmax^2-2*omega^2)^(1/2)-1, t = 0 .. Theta(t)) = 0

(22)

Sol[1]

Intat(1/(2*omega^2*cos(_a)+Vmax^2-2*omega^2)^(1/2), _a = Theta(t))-t = 0

(23)

"Using  ( 1-cos(theta))/(2)=sin(theta/(2))^(2)and substituting by hand"

NotsoSHM := Intat(1/(Vmax*sqrt(1-2*omega^2*sin((1/2)*_a)^2/Vmax^2)), _a = (1/2)*Theta(t))-t = 0

Intat(1/(Vmax*(1-2*omega^2*sin((1/2)*_a)^2/Vmax^2)^(1/2)), _a = (1/2)*Theta(t))-t = 0

(24)

``

``


 

Download SHM_and_not_so_SHM.mw

I am practicing with some diff equations. I am having problem solving for one of the constants. I am having a pproblem assigning a value to derivatives or 2nd derivatives. What is a good general technique is this type of situation?
 

restart

NULL

``

omega^2 = g/l

omega^2 = g/l

(1)

Eq1 := diff(Theta(t), t, t) = -omega^2*Theta(t)

diff(diff(Theta(t), t), t) = -omega^2*Theta(t)

(2)

ics := Theta(0) = 0, (diff(Theta(t), t))(0) = Vmax, (diff(Theta(t), t, t))(0) = 0

Theta(0) = 0, (diff(Theta(t), t))(0) = Vmax, (diff(diff(Theta(t), t), t))(0) = 0

(3)

SHM := dsolve({Eq1, ics})

(4)

SHM := dsolve({Eq1})

{Theta(t) = _C1*sin(omega*t)+_C2*cos(omega*t)}

(5)

SHM := dsolve({Eq1, Theta(0) = 0})

Theta(t) = _C1*sin(omega*t)

(6)

``

diffSHM := diff(SHM, t)

diff(Theta(t), t) = _C1*omega*cos(omega*t)

(7)

``

(Theta(t))(0) = 0, (diff(Theta(t), t))(0) = V

(Theta(t))(0) = 0, (diff(Theta(t), t))(0) = V

(8)

``

``

``

``

``

NULL

NULL


 

Download SHM.mw

In the test package below I want the the Value of Clr to be "B" when the package is loaded. How do I achieve that?
 

restart

mylibdir := cat(kernelopts(homedir), kernelopts(dirsep), "maple", kernelopts(dirsep), "toolbox", kernelopts(dirsep), "personal", kernelopts(dirsep), "lib")

"C:\Users\Ronan.Ronan-PC\maple\toolbox\personal\lib"

(1)

``

libname := mylibdir, libname

"C:\Users\Ronan.Ronan-PC\maple\toolbox\personal\lib", "C:\Program Files\Maple 2016\lib", "C:\Users\Ronan.Ronan-PC\maple\toolbox\personal\lib"

(2)

``

``

``

"RTest:=module()  option package;  export  Sums;    global Clr;  Clr:=B;  Sums:=proc(p1,p2,c:=Clr)  if c=B or c=b  then    p1+p2  elif c=G or c=g then  p1-p2  elif c=R or c=r  then      if p2 =0 then "Not Valid"       else ( p1)/(p2)        end if  else "Error"  end if  end proc;    end module; "

_m655171968

(3)

``

savelib('RTest')

restart

``

with(RTest)

[Sums]

(4)

"At This point I want the value of Clr to be automaticially   B"

Sums(2, 3)

"Error"

(5)

RTest:-Sums(2, 3, b)

5

(6)

``

RTest:-Sums(2, 3, r)

2/3

(7)

RTest:-Sums(2, 3, g)

-1

(8)

Clr := g

g

(9)

RTest:-Sums(2, 3)

-1

(10)

RTest:-Sums(2, 3, b)

5

(11)

RTest:-Sums(2, 3)

-1

(12)

RTest:-Sums(2, 0, r)

"Not Valid"

(13)

``


 

Download Module_Test_global_Var.mw

Trying to write a generat purpose procedure insteat of having 3 or 4 different named procceduers.

Need to determine the input types of say A,B,C

Proc(A,B,C)

1) A,B,C could be for the form 3/2 , 5x-7 , x^2-sqrt(x+3)  i.e numbers or formulas

2) A,B,C could be 2 elenent lists [2,3]  , [5x-6y,8x+2] ,[2,sqrt(3)]  i.e 2D points

3) A,B,C could be 3 element lists as above    i.e 3D points

4) A,B,C could be 2D vectors

5) A,B,C could be 3D vectors

A, B, C will not be of mixed types but would be good to check A, B, C for consistency and if not retrun an error

Looking to calculate output based on

If type 1) ......

elif type 2).....

.

.

elif type 5)...

end if

return.....

end proc

 

 

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