I am tryng to write and solve within Maple the equations of movement for a single body subject to a gravitatinal field, F_=-GMm/r2

But I get an error message when trying to define the Angular Momentum which doesn't make sense for me.

Thank you for any help on this topíc.

restart; with(Physics[Vectors]); conventions, Setup(mathematicalnotation = true);
conventions, [mathematicalnotation = true]
r_ := rho*_rho;
r_ := rho _rho
_rho(t);
_rho(t)
rho(t);
rho(t)
v_ := diff(rho(t)*_rho(t), t);
/ d \ / d \
v_ := |--- rho(t)| _rho(t) + rho(t) |--- phi(t)| _phi(t)
\ dt / \ dt /
a_ := diff(%, t);
/ 2 \
| d | / d \ / d \
a_ := |---- rho(t)| _rho(t) + 2 |--- rho(t)| |--- phi(t)| _phi(t)
| 2 | \ dt / \ dt /
\ dt /

/ 2 \ 2
| d | / d \
+ rho(t) |---- phi(t)| _phi(t) - rho(t) |--- phi(t)| _rho(t)
| 2 | \ dt /
\ dt /

eq[1] := -G*M*_rho(t)/r^2-a_ = 0;
/ / 2 \ 2\
| G M | d | / d \ |
eq[1] := _rho(t) |- --- - |---- rho(t)| + rho(t) |--- phi(t)| |
| 2 | 2 | \ dt / |
\ r \ dt / /

/ / 2 \
| / d \ / d \ | d |
+ _phi(t) |-2 |--- rho(t)| |--- phi(t)| - rho(t) |---- phi(t)|
| \ dt / \ dt / | 2 |
\ \ dt /

\
|
| = 0
|
/
Eq[1, 2] := seq(Component(lhs(eq[1]), n) = 0, n = 1 .. 2);
/ 2 \ 2
G M | d | / d \
Eq[1, 2] := - --- - |---- rho(t)| + rho(t) |--- phi(t)| = 0,
2 | 2 | \ dt /
r \ dt /

/ 2 \
/ d \ / d \ | d |
-2 |--- rho(t)| |--- phi(t)| - rho(t) |---- phi(t)| = 0
\ dt / \ dt / | 2 |
\ dt /
NULL;

L_ := `&x`(r_, m*v_);
Error, (in Physics:-Vectors:-&x) found the unit vector _rho present also as a function _rho(t); either one form or the other - not both - can be present in an algebraic expression

HI, I am trying to solve two PDEs but in boundry conditions there is arising an error plz help.
Nazi.mw

Hi,

I recently noticed that Maple 2015 has become irresponsive on mac (macbook pro) with the latest java release (Java 8 update 66). Did anywone experience the same problem ?

Hi,

I have a first order differential eq. for some variable say $r(x)$, where $x$ is the independent variable.

After solving this differential equation numerically, I want to use its solution in other expression for $r(x)$ and plot the expession with $x$.

Please let me know how to do it.

Thanks in advance.

I'm trying to use the CodeGeneration package to generate code for a series expansion. I'd like to wrap it in a function that specifies the arguments, so that the code generation package can generate a complete function definition along with definitions for all the temporary variables.

with(CodeGeneration):
f := proc(r): x->r end proc:
to_translate := f(convert(series(sin(x),x,20),polynom));

to_translate := proc (x) options operator, arrow; x-(1/6)*x^3+(1/120)*x^5-(1/5040)*x^7+(1/362880)*x^9-(1/39916800)*x^11+(1/6227020800)*x^13-(1/1307674368000)*x^15+(1/355687428096000)*x^17-(1/121645100408832000)*x^19 end proc

CodeGeneration['C']( to_translate );

Warning, procedure/module options ignored
double to_translate (double x)
{
  return(r);
}

Instead of using the value for 'r' passed in, CodeGenerate is producing a function which returns the bare symbol 'r' which is treated as a double. It shouldn't be an issue with lazy evalution because 'to_translate' is evaluated on the statement before the call to CodeGeneration, and to_translate has the full expression that I want to generate code for. How do I get CodeGeneration to produce the intented result?

psi = x^(4/5)*f(x, eta)/(1+x)^(1/20)

eta = y/(x^(1/5)*(1+x)^(1/20))

how can i (diff(psi, x))

how can i (diff(psi, y))

Has anyone solved this problem from an older Putnam paper?

An ellipse sitting in the first quadrant with its major axis parallel to the x axis is tangent to the positive x and y axes.

It slides clockwise within the first quadrant while maintaining tangency to both positive axes until its major axis is parallel to the y axis.

Prove that the locus of its centre is the arc of a circle.

I have crudely animated this motion by sliding the axes around the stationary ellipse. Is there a more elegant animation which slides the ellipse against stationary axes?

I have functions like

g := (y, t)->sin(y(t))

diff(g(y, t), t) # ok

How to determine the derivative below with maple :

diff(g(y, t), y(t))

Thanks

Hi everyone,

Can anybody help me to write a programme in maple? I want to do a loop that iterate from an integer from 0 to N where I want to write a prodedure, say, MEC(N). Then I want to organise the output into a list of three lists  [[min points],[escape],[capture]], which, if correct, should include all integers from 0 to N exactly once.

> MEC := proc (N)
local IsEmpty, Escape, escape, capture, minpoints, Capture, z, MinPts, ic;
IsEmpty := array(0 .. 2*N);
Escape := array(0 .. 2*N);
Capture := array(0 .. 2*N);
MinPts := array(0 .. N);
IsEmpty := true;
Escape := true;
Capture := true;
MinPts := true;

for ic from 0 to N do
if IsEmpty then
z := ic;
MinPts[ic] := true;
z := ic;
while z <= 2*N and F(z) <= 2*N do
z := F(z);
IsEmpty[z] := true;
Escape[z] := true
end do;

z := ic;
while z <= 2*N and Finv(z) <= 2*N do
z := Finv(z);
IsEmpty[z] := true;
Capture[z] := true end do fi;
end do;
return [MinPts(z), Escape(z), Capture(z)]
end proc;

There are two operations involved in the program which is the function F and F inverse called Finv. 
i need to produce the output which contain the list of integers exactly once.

I could not figure out which logical expression that I do wrong.

Thank you for your help!

How to find the value of alpha and beta?

thank you for helping

Download Qu_3.mw

Just a simple little proc that grabs and displays some simple data for general stars (I've only listed a couple for starters).  It wasn't till later that I realized it's not an up to date database as it doesn't contain more recent interesting stars like Kepler 452.  One would have to go to the SIMBAD astronomical database for which I have not yet devoted any time for .. at least not yet. 

Download StarData3.mw

How evaluate system of two integral equation by laplace transform ?

Download Qu_2_mapel.mwQu_2_mapel.mw

Hello everyone!

i want to make a triangle which height's is a. Sorry, my English is not very good!

And I writed it by C language, but It is not right in maple. and I don't know. Can you help me? thank you very much! triangle.mw

Hi all,

How can the black circle be visible?

Visible also below the 3D graph?

Best, perr7

B := spacecurve( [R*cos(t),R*sin(t),0] ,t=0..4*Pi,thickness=1, style=line, color=black);

animate( plot3d, [     P_Pi2(x,y,t)  ,  x=-4000..4000,y=-4000..4000 ], t=0..1, frames=10, transparency=0, style=surfacewireframe, labelfont=[times, roman, 25], orientation=[45,60,0], view=[-4000..4000, -4000..4000, 0..0.006], caption=typeset( theta=Pi/2 ) , axesfont=[times, 15], axes=frame, background=B   );

It's my first post on this forum so Hi everyone from Poland!

I have the following question.

Is it possible to force the Maple to obtain a result in a particular form? For example instead (a+b)³ I wan to have the result of the form: a³+3a²b+3ab²+b³. And I want to multiply the red brackets to receive a quadratic forms.

Below is a sample result that I get and I want it in a different form.

http://i65.tinypic.com/28k29hk.png

[IMG]http://i65.tinypic.com/28k29hk.png[/IMG]