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Results tagged with classical-mechanics
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user 12617
Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.
3
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0
answers
174
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What happens when Appell-Chetaev's rule for constrained mechanical systems is not applicable?
Background:
Let be given a mechanical system whose configuration space is a manifold $Q$, and the kinetic energy is a metric $K$ on $Q$, in presence of a potential function $V$.
Let us identify the ta …
- 4,306
5
votes
3
answers
2k
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The Lagrangian formulation of mechanics without going through variational principles.
In some texts on classical mechanics and not only, the Euler--Lagrange equations of motion are directly obtained as solution of variational problems.
On the other side, sometimes reading about hamilto …
- 4,306
2
votes
0
answers
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In search for a more geometric proof of a result of van der Schaft and Maschke on nonholonom...
Edit: Now I have found something that appears to answer my own question. It is section 2 in the paper "On Submanifolds and Quotients of Poisson and Jacobi Manifolds" by Ch.-M. Marle. (There, he transf …
- 4,306
6
votes
1
answer
1k
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How the Jacobi metrics may be useful in mechanics with or without constraints?
A mechanical system $(Q,K,V)$ is specified by the configuration space $Q,$ the potential energy $V\in C^\infty(Q),$ and the kinetic energy $K=K_g$ given by a Riemannian metric $g$ on $Q.$
If $V{<}e$ …
- 4,306
20
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4
answers
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What is the role of contact geometry in the hamiltonian mechanics?
Let us assume someone is interested in the study of Hamiltonian mechanics.
What are good examples to illustrate him of the usefulness of contact geometry in this context?
On one hand the Hamiltonian …
- 4,306