Singularities of the Hamiltonian vectorfield in nonautonomous variational problems

✍ Scribed by Helena Mena-Matos

• Book ID: 104151038
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 319 KB
• Volume: 283
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(03)00303-2

✦ Synopsis

Variational problems with n degrees of freedom give rise (by Pontriaguine maximum principle) to a Hamiltonian vectorfield in T * R n , that presents singularities (nonsmoothness points) when the Lagrangian is not convex. For one degree of freedom nonautonomous problems of the calculus of variations where the Hamiltonian vectorfield in T * R depends explicitly on the time, we consider the associated autonomous vectorfield in T * R × R and classify its singularities up to an equivalence that takes into account the special role played by the time coordinate, i.e., that respects the foliation of T * R × R into planes of constant time.