# Is the principle of minimum action applicable to nonholonomic systems?

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1. Oct 29, 2014

### ORF

Hello

Is the principle of minimum action applicable to nonholonomic systems? Why?

If this question is already answered in this forum, just tell me, and I will delete this thread.

Thank you for your time :)

Greetings
PS: My mother language is not English, so I'll be glad if you correct any mistake.

2. Oct 30, 2014

### ORF

Sorry, that was an old expression; the modern one is "principle of least action" (or stationary action).

Greetings.

3. Nov 1, 2014

### ORF

It is known as Hamilton's principle in classical mechanics :)

Greetings.

4. Nov 1, 2014

### atyy

I googled the terms, and found

http://www.ingvet.kau.se/juerfuch/kurs/amek/prst/11_nhco.pdf

http://www2.cds.caltech.edu/~blochbk/mechanics_and_control/survey/2005-02-07_survey_fullrefs.pdf.
"There are some fascinating differences between nonholonomic systems and classical Hamiltonian or Lagrangian systems. Among other things: Nonholonomic systems are nonvariational - they arise from the Lagrange-d'Alembert principle and not from Hamilton's principle; while energy is preserved for nonholonomic systems, momentum is not always preserved for systems with symmetry (i.e., there is nontrivial dynamics associated with the nonholonomic generalization of Noether's theorem); nonholonomic systems are almost Poisson but not Poisson (i.e., there is a bracket which together with the energy on the phase space defines the motion, but the bracket generally does not satisfy the Jacobi identity); and finally, unlike the Hamiltonian setting, volume may not be preserved in the phase space, leading to interesting asymptotic stability in some cases, despite energy conservation."

5. Nov 1, 2014

### ORF

Hello

Thank you so much for the links. I didn't know that this issue was so complex :)

Greetings.