It is shown how a standard public-domain program for the numerical continuation of stationary and periodic solutions of dynamical systems, and of their bifurcations, can be used to analyse the behaviour of solutions of the equations of motion for a multibody system. The equations of motion are derived with the aid of a symbolic multibody program. From these, the variational equations and the derivatives with respect to parameters can be easily obtained with the underlying algebraic manipulation routines. The analysis procedure is illustrated in the example of a double pendulum, where some results can be checked against analytically derived results.
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Numerical Continuation Methods and Bifurcation Analysis Applied to Multibody System Dynamics
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Meijaard, JP. "Numerical Continuation Methods and Bifurcation Analysis Applied to Multibody System Dynamics." Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C. Chicago, Illinois, USA. September 2–6, 2003. pp. 63-70. ASME. https://doi.org/10.1115/DETC2003/VIB-48310
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