Publication: Geometric Hamilton-Jacobi theory for systems with external forces
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To cite this item, use the following identifier: https://hdl.handle.net/10016/37366
Abstract
In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems, and present some examples. Additionally, we present a method for the reduction and reconstruction of the Hamilton-Jacobi problem for forced Hamiltonian systems with symmetry. Furthermore, we consider the reduction of the Hamilton-Jacobi problem for a Caplygin system to the Hamilton-Jacobi problem for a forced Lagrangian system.
Note
We thank the referee for his/her constructive comments. The authors acknowledge financial support from the Spanish Ministry of Science and Innovation (MICINN) under Grant No. PID2019-106715GB-C21 and "Severo Ochoa Programme for Centres of Excellence in R&D" (Grant No. CEX2019-000904-S). Manuel Lainz wishes to thank MICINN and the Institute of Mathematical Sciences (ICMAT) for the FPI-Severo Ochoa predoctoral contract (No. PRE2018-083203). Asier López-Gordón would like to thank MICINN and ICMAT for the predoctoral contract (No. PRE2020-093814). He is also grateful for enlightening discussions on fiber bundles with his friend and colleague Alejandro Pérez-González
Bibliographic citation
León, M. de; Lainz, M.; & López-Gordón, A. (2022). Geometric Hamilton–Jacobi theory for systems with external forces. Journal of Mathematical Physics, 63(2), 022901.