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A Geometric Derivation of the Equations of Motion for Mechanical Systems With Scleronomic Constraints

[+] Author Affiliations
Sotirios Natsiavas, Elias Paraskevopoulos

Aristotle University, Thessaloniki, Greece

Paper No. DETC2015-46618, pp. V006T10A029; 10 pages
doi:10.1115/DETC2015-46618
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5716-8
  • Copyright © 2015 by ASME

abstract

A new set of equations of motion is presented for a class of mechanical systems subjected to equality motion constraints. Specifically, the systems examined satisfy a set of holonomic and/or nonholonomic scleronomic constraints. The main idea is to consider the equations describing the action of the constraints as an integral part of the overall process leading to the equations of motion. The constraints are incorporated one by one, in a process analogous to that used for setting up the equations of motion. This proves to be equivalent to assigning appropriate inertia, damping and stiffness properties to each constraint equation and leads to a system of second order ordinary differential equations for both the coordinates and the Lagrange multipliers associated to the motion constraints automatically. This brings considerable advantages, avoiding problems related to systems of differential-algebraic equations or penalty formulations. Apart from its theoretical value, this set of equations is well-suited for developing new robust and accurate numerical methods.

Copyright © 2015 by ASME

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