| Title:
|
On D’Alembert’s Principle (English) |
| Author:
|
Bates, Larry M. |
| Author:
|
Nester, James M. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
19 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
57-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory. (English) |
| Keyword:
|
nonholonomic constraints |
| Keyword:
|
d’Alembert’s principle |
| MSC:
|
37J60 |
| MSC:
|
70F25 |
| MSC:
|
70H33 |
| MSC:
|
70H45 |
| idZBL:
|
Zbl 06010915 |
| idMR:
|
MR2855391 |
| . |
| Date available:
|
2011-10-31T08:14:29Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141679 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Cushman, R., Kempainen, D., Śniatycki, J.: A classical particle with spin realized by reduction of a nonlinear nonholonomic constraint.Reports on mathematical physics 41 (1) 1998 133–142 MR 1617882 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[9] Koon, W., Marsden, J.: Poisson reduction for nonholonomic mechanical systems with symmetry.Reports on mathematical physics 42 1998 101–134 Zbl 1120.37314, MR 1656278 |
| Reference:
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[10] Krupková, O., Musilová, J.: The relativistic particle as a mechanical system with non-holonomic constraints.J. Phys. A: Math. Gen. 34 2001 3859–3875 MR 1840850, 10.1088/0305-4470/34/18/313 |
| Reference:
|
[11] Marle, C.-M.: Various approaches to conservative and nonconservative nonholonomic systems.Reports on mathematical physics 42 1998 211–229 Zbl 0931.37023, MR 1656282 |
| Reference:
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[12] Rosenberg, R.: Analytical dynamics of discrete systems.Plenum press 1997 MR 0512893 |
| Reference:
|
[13] Śniatycki, J.: Orbits of families of vector fields on subcartesian spaces.Annales de L’Institut Fourier 53 2003 2257–2296 Zbl 1048.53060, MR 2044173, 10.5802/aif.2006 |
| Reference:
|
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| . |
