Analytical Solution of ODE from Making Them Move (Requested)

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From: John David Funge
Date: Tue, 05 Jan 1993 21:28

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In Chapter 14 (Using Dynamics in Computer Animation: Control 
and Solution Issues by Mark Green) of Making Them Move edited 
by Badler, Barsky & Zelter the following sets of equations are
given.

Linear Equations:

m1 q1'' + c1 q1' + c2(q1' - q2') + k1 q1 + k2(q1 - q2) = F1
m2 q2'' + c2(q2' - q1') + k2(q2 - q1) = F2

Non-linear Equations:

m1 q1'' + c1 q1' + c2(q1' - q2') + k1 q1 - k2[(q2 - q1) + 0.5(q2 - q1)^3] = F1
m2 q2'' + c2(q2' - q1') + k2[(q2 - q1) + 0.5(q2 - q1)^3] = F2

m1, m2, c1, c2, k1, k2, F1, F2 are constants.

The text states that these equations have analytical solutions and
gives Advanced Dynamics by D'Souza, A.F. and V.K. Garg (1984) as 
a reference.

I have been unable to obtain a copy of Advanced Dynamics, so if
any one can provide me with the analytical solutions to the above
equations I would be grateful (funge@dgp.toronto.edu).

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Path: arc1-ca.pugleaf.net!sparky!uunet!usc!cs.utexas.edu!torn!utcsri!dgp.toronto.edu!funge
Newsgroups: comp.theory.dynamic-sys,comp.graphics.animation
From: funge@dgp.toronto.edu (John David Funge)
Subject: Analytical Solution of ODE from Making Them Move (Requested)
Message-ID: <1993Jan5.162836.13236@jarvis.csri.toronto.edu>
Organization: CSRI, University of Toronto
Date: 5 Jan 93 21:28:36 GMT
Lines: 25