
ISSN:
1941-4889
eISSN:
1941-4897
Journal of Geometric Mechanics
December 2020 , Volume 12 , Issue 4
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In this paper, we characterize multiply warped product semi -Riemannian manifolds when the base is conformal to an
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the configuration space and described by the continual equation of motion and the continuity equation. For Hamiltonian systems, the usual Hamilton-Jacobi equations naturally follow from this theory. The proposed formulation of the Hamilton-Jacobi theory, as the theory of ensemble, allows interpreting in a natural way the transition from quantum mechanics in the Schrödinger form to classical mechanics.
In this paper, we show that the spaces of sections of the
In this work we introduce a category
This paper extends the theory of controlled Hamiltonian systems with symmetries due to [
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