Message Boards Message Boards

Help using NDSolve for an orbital dynamics problem

Hi all,

I am new to Mathematica and I am trying to model an asymmetric momentum exchange tether in its orbit about the Earth. The tether initially starts as a symmetrical system and simply has the ability to alter the tether lengths to change the CoM and thus account for mass discrepancies causing the system to act asymmetrically.

The problem I am receiving is that I am passing three equations to NDsolve. NDsolve accepts the equations as differential equations, and despite providing both boundary and initial conditions to the solver NDsolve is not resulting in a valid list of rules or a dispatch table and thus cannot be used for further evaluation of parameters to plot. I have attached a copy of my most "up to date" model, please forgive me if it is something blaringly obvious, I have been staring at my screen for a considerable amount of time now.

If there is any other information you need please let me know.

POSTED BY: Jameel Cathcart
5 Replies
Sort By:

The third equation simplifies to

\[Theta]''[t] + \[Psi]''[t] == 0

as I said. The second equation is not a differential equation. The first equation contains the factor \[Theta]''[t] + \[Psi]''[t]: if we replace it with zero, also the first equation ceases to be a differential equation.
POSTED BY: Gianluca Gorni

Right so none of the equations are actually differential equations??

Your assistance is most appreciated by the way so thank you!
POSTED BY: Jameel Cathcart

The third equation is differential.
POSTED BY: Gianluca Gorni

If I am not mistaken, your three equations eqn1 == 0, eqn2 == 0, eqn3 == 0 are rather strange. The third one is

\[Theta]''[t] + \[Psi]''[t] == 0

If you replace this into the first and second equation you get a system of two algebraic equations in the two variables R[t] and \[Psi][t], which would seem to imply that R[t] and \[Psi][t] are constants.
POSTED BY: Gianluca Gorni

Apologies, I realise this notebook I uploaded pre-loaded the numerical values into the equations. This is how the Lagrange Equations of motion look once they have been differentiated enter image description here

R[t] is the radial position of the tether in its orbit about the earth - this is confined to a circular orbit so in -fact yes it would be constant. Does this mean that equation 2 (which is the lagrange equation in wrt R[t]) is unnecessary and overcomplicates the system?

Psi[t] is the angular displacement of the tether in the orbital plane as it rotates "end over end" and theta[t] is the true anomaly of the system in its orbit

POSTED BY: Jameel Cathcart
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract