scholarly journals Helmholtz conditions and symmetries for the time dependent case of the inverse problem of the calculus of variations

2010 ◽  
Vol 60 (11) ◽  
pp. 1710-1725 ◽  
Author(s):  
Ioan Bucataru ◽  
Oana Constantinescu
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Time Dependent ◽  
Dependent Case ◽  
Helmholtz Conditions

Feynman's Proof of the Lorentz Force Equations with Dissipation Linear in the Velocity

1997 ◽  
Vol 12 (33) ◽  
pp. 2523-2533
Author(s):  
S. K. Soni ◽  
Simmi Singh
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Lorentz Force ◽  
Linear Dependence ◽  
Velocity Vector ◽  
Equations Of Motion ◽  
Type Form ◽  
Helmholtz Conditions ◽  
Dissipative Terms ◽  
Lorentz Force Law

We present the Feynman proof of the Lorentz force law plus dissipative terms with a linear dependence on the velocity vector. In addition, we discuss in this context the inverse problem of the calculus of variations and the inverse problem for the Poisson dynamics. Given the equations of motion, the Helmholtz conditions for the inverse problem of the calculus of variations are solved and the Lagrangian is shown to have the nonsingular gauge type form.

Sign in / Sign up

Export Citation Format

Share Document