Nonlinear Dynamics

, Volume 88, Issue 2, pp 1093–1097 | Cite as

Hamilton’s principle and Hamilton’s equations with holonomic and non-holonomic constraints

Original Paper


Hamilton’s Principle is written in terms of generalized displacements and momenta. This allows holonomic and non-holonomic constraints to be treated on an equal basis using Lagrange multipliers to derive equations of motion for a dynamical system. Three examples are considered that have been previously considered in the literature by other methods.


Hamilton’s principle Hamilton’s equations of motion Non-holonomic constraints 


  1. 1.
    Udwadia, F.E.: Constrained motion of hamiltonian systems. Nonlinear Dyn. 83, 1–11 (2016)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Duke UniversityDurhamUSA

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