Lagrangian Formulation
Instead of a Hamiltonian, a
Lagrangian
formulation can be used, in which case Lagrange’s equation is solved:
Lagrange’s equation is rearranged before solving into the following form:
where
N
is the Hessian of the Lagrangian with respect to the velocities:
For a more in-depth example, see
Choosing a Formulation
in the
Particle Tracing Modeling
chapter.