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La La geometría del problema inverso de la mecánica lagrangiana
- Autor/a
- Castaño Garrido, Francisco Manuel
It's well known that the Euler-Lagrange equations, which are the basis of classical mechanics, can be obtained from Hamilton’s variational principle. This variational formulation is very important in theorical physics. The inverse problem of lagrangian mechanics consists of: finding out when we can associate a variational principle to a given system of second order diferencial equations, namely find out if the given system can be obtained as the Euler-Lagrange equations of a certain lagrangian. This problem is characterised by the existence of a function matrix verifying the famous Helmholtz (1821-1894) conditions. The objective of this dissertation is to analyze the problem from a geometric point of view, and arrive to a free coordinate version of Helmholtz conditions. This memory can be considered as a possible extension of part of the knowledge obtained in the subject of the Master in Mathematics: Mathematical methods of Physics.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 29/05/2018
- Serie
- 134a Publicaciones del Departamento de Geometría y Topología
- ISBN
- 9788489390515
- Availability
- Si
It's well known that the Euler-Lagrange equations, which are the basis of classical mechanics, can be obtained from Hamilton’s variational principle. This variational formulation is very important in theorical physics. The inverse problem of lagrangian mechanics consists of: finding out when we can associate a variational principle to a given system of second order diferencial equations, namely find out if the given system can be obtained as the Euler-Lagrange equations of a certain lagrangian. This problem is characterised by the existence of a function matrix verifying the famous Helmholtz (1821-1894) conditions. The objective of this dissertation is to analyze the problem from a geometric point o