Action principles for dissipative, non-holonomic Newtonian mechanics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909233404968960 |
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| author | Acharya, Amit Sengupta, Ambar N. |
| author_facet | Acharya, Amit Sengupta, Ambar N. |
| contents | A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and positions, is presented. Methods for incorporating constraints are critically assessed. General theory, as well as explicitly worked out variational principles for a dissipative system (due to Lorenz) and a system with anholonomic constraints (due to Pars) are demonstrated. Conditions under which a (family of) dual Hamiltonian flow(s), as well as a constant(s) of motion, may be associated with a conservative or dissipative, and possibly constrained, primal system naturally emerge in this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10616 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Action principles for dissipative, non-holonomic Newtonian mechanics Acharya, Amit Sengupta, Ambar N. Mathematical Physics Dynamical Systems Classical Physics A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and positions, is presented. Methods for incorporating constraints are critically assessed. General theory, as well as explicitly worked out variational principles for a dissipative system (due to Lorenz) and a system with anholonomic constraints (due to Pars) are demonstrated. Conditions under which a (family of) dual Hamiltonian flow(s), as well as a constant(s) of motion, may be associated with a conservative or dissipative, and possibly constrained, primal system naturally emerge in this work. |
| title | Action principles for dissipative, non-holonomic Newtonian mechanics |
| topic | Mathematical Physics Dynamical Systems Classical Physics |
| url | https://arxiv.org/abs/2306.10616 |