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A Flexible Multibody Pantograph Model for the Analysis of the Catenary–Pantograph Contact Read chapter Read first chapter

2011 | OriginalPaper | Chapter

Energy Considerations for the Stabilization of Constrained Mechanical Systems with Velocity Projection

Authors : Juan C. García Orden, Roberto A. Ortega Aguilera

Published in: Multibody Dynamics

Publisher: Springer Netherlands

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Abstract

There are many difficulties involved in the numerical integration of index-3 Differential Algebraic Equations (DAEs), mainly related to stability, in the context of mechanical systems. An integrator that exactly enforces the constraint at position level may produce a discrete solution that departs from the velocity and/or acceleration constraint manifolds (invariants). This behaviour affects the stability of the numerical scheme, resulting in the use of stabilization techniques based on enforcing the invariants. A coordinate projection is a poststabilization technique where the solution obtained by a suitable DAE integrator is forced back to the invariant manifolds. This paper analyzes the energy balance of a velocity projection, providing an alternative interpretation of its effect on the stability and a practical criterion for the projection matrix selection.

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previous chapter Application of General Multibody Methods to Robotics
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Footnotes
1
Not necessarily the same employed for the velocity projection.
 
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Metadata
Title
Energy Considerations for the Stabilization of Constrained Mechanical Systems with Velocity Projection
Authors
Juan C. García Orden
Roberto A. Ortega Aguilera
Copyright Year
2011
Publisher
Springer Netherlands
Book
Multibody Dynamics

Print ISBN: 978-90-481-9970-9

Electronic ISBN: 978-90-481-9971-6

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-90-481-9971-6_8

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