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Ronan

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14 years, 32 days
East Grinstead, United Kingdom
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Non Simple Harmonic Pendulum Motion. Dif...

Ronan 1401 Maple 2016
January 23 2017
2 1

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

How to solve for constants Deriving Simp...

Ronan 1401 Maple 2016
constants
January 22 2017
1 3

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

How to set a globals default value for a...

Ronan 1401 Maple 2016
package module default
December 27 2016
1 2

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

How to Test Input Typed to a Procedure ...

Ronan 1401 Maple 2016
October 18 2016
4 8

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

 

 

Help File edit after storing in a databa...

Ronan 1401 Maple 2016
October 12 2016
1 4

I am experimenting with creating help files for  my own package.

I have saved  a package overview file and one package command  file into a help data base as a test usingTools, Help Database, Save as Help Page.

These 2 help pages work in principle as i can find them when I search for them and the command  help page opens from the overview page. I now need to edit them. So I edit the original worksheets and use Tools, Help Database, Save as Help Page to update the data base.

Now Maple will not let me overwrite the original page.The Help file savy you can overwrite. So I have to delete the original page first then resave it back in. This involves reentering all the data again. Topic Alisies and Table of contents.

To say the least this is extremely tedious  vastly innefficient and very error prone. I will have upto say 40 help pages to edit and they will require some expirementing with.

Is there a better way to do this?

Edit:-

Hve added this line the the bottom of the worksheet

makehelp('`Rational Trigonometry`', "Rational Trigonometry Overview Help.mw", " C:\Users\Ronan.Ronan-PC\maple\toolbox\UserHelp\lib\maple.help")

get     Error, (in readline) file or directory does not exist

 

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