Equivalent lagrangians and the inverse problem in classical mechanics

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:6313828

Pardo Orive, F P.J.

The Inverse Problem consists mainly in determining whether the set of solutions of a given set of differential equations is also the set of stationary curves of a variational problem based on an Action Integral. The Restricted Inverse Problem consists in determining if a given set of differential equations coincides with the set of Euler-Lagrange equations of a certain Lagrangian L. The most important form of the solution to this problem came in 1887, when Helmholtz established a set of necessary and sufficient conditions for a set of second-order differential equations to be derivable from a Lagrangian. This dissertation analyzes the role that the Helmholtz conditions play in the proof of the Trace Theorem, showing that not all the information contained in the Helmholtz conditions is used to prove the theorem. The author also consider some examples of second-order differential equations. He also analyses the Inverse Problem in Generalized Dynamics. An alternative approach to the Inverse Problem in Classical Mechanics is described, showing that the Helmholtz conditions can be transformed into a single relation over a set of functionally independent constants of motion.

• Research Organization: Texas Univ., Austin (USA)
• OSTI ID: 6313828
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
DYNAMICS
EQUATIONS
FUNCTIONS
HELMHOLTZ THEOREM
LAGRANGIAN FUNCTION
MECHANICS
MOTION
VARIATIONAL METHODS