In Hamilton-Jacobi formul
In Hamilton-Jacobi formulation of mechanics, Hamilton's principal function depends on the integral of this quantity with respect to a generalized position. The derivative of the Lagrangian with respect to a generalized velocity gives the generalized form of this quantity, whose generalized form's time derivative appears in one of Hamilton's equations. The free particle Hamiltonian is proportional to this quantity (*) squared divided by the mass. Newton's Second Law can be stated in terms of the change in this quantity as that change is equal to the net force. Conserved in both elastic and inelastic collisions, for 10 points, is which vector quantity often denoted p, and defined as mass times velocity?
In Hamilton-Jacobi formulation of mechanics, Hamilton's principal function depends on the integral of this quantity with respect to a generalized position.
linear momentum [do not accept angular momentum]