Perplexing NDSolve error message
- To: mathgroup at smc.vnet.net
- Subject: [mg42227] Perplexing NDSolve error message
- From: Ravi Balasubramanian <ravib at andrew.cmu.edu>
- Date: Tue, 24 Jun 2003 01:27:15 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear MathGroup readers, I am trying to solve a Lagrangian dynamics (mechanical system) problem, where the dimension of the sytem's configuration (theta1, theta2, theta3, phi1, phi2) is five and the system has no external inputs. Thus, there are five second order, non-linear DEs to be solved simultaneously. In the code attached, I have derived the Lagrangian dynamics and tried to solve it using NDSolve for one particular initial condition. Mathematica (v4.2) gives me the following error messages: Solve::svars: Equations may not give solutions for all "solve" variables. NDSolve::"ndnum": "Encountered non-numerical value for a derivative at \ \!\(t\) == \!\(2.4663267130000377`*^175\)." 1) I am fairly confident there is a solution to this system, since if I plug in the initial conditions into the equations, I get the second derivatives of all five configuration elements to be zero ( This can be verified by using "Solve" to solve for the second derivatives when the equations are evaluated at t = tMin using the initial conditions.) Thus, the state of the system does not change, and the solution shd just be the same as the initial conditions. 2) Another perplexing part of the output is that Mathematica is looking outside the interval of [tMin, tMax]. It's pointing out that it can't find a numerical value of the derivatives at t = 2*10^175! I wonder why its looking out of the bounds. 3) Is there a way of stepping through or debugging NDSolve manually? I will appreciate it greatly if someone can give some clues as to what the error message means and what I might be doing wrong. If you need more info, you can contact me at ravib at cmu.edu. Thanks! For those who would like some physical understanding of the system: The system is a hemisphere pivotted at its body center. The sphere has two legs hinged along a diameter. The legs may rotate about axes pointing along the diameter. The legs have small masses at their distal ends, and the sphere has masses attached to its body at the locations where the legs are hinged. The idea is to study how the body rolls, yaws, and pitches when the legs are moved. Since, in the above example, there are no external torques, the system is influenced only by gravity. At the configuration (0,0,0,-Pi/2, -Pi/2), the hemisphere masses are horizontal, and the legs are vertical. Thus, there shd be no change in the state. Ravi Balasubramanian, Carnegie Mellon University, Pittsburgh, PA.