Some Applications of Affine in Velocities Lagrangians in Two-Dimensional Systems

Abstract

The two-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for the system of differential equations. We illustrate our analysis with several examples of families of forces that are relevant in mechanics, on one side, and of some relevant biological systems, on the other.

Keywords

• affine Lagrangians
• inverse problems
• Jacobi multipliers
• Hamiltonian formulation
• mechanical and biological systems