Representing the sum of all kinetic and potential energies of the aforementioned dynamic system, FTP, identify this function named for the Irish mathematician who discovered it.
It was originally introduced to express the rate of change in time of the condition of a dynamic physical system - one regarded as a set of moving particles.  If the Einstein summation has been used, then it can be defined as q, the generalized coordinate, times p, generalized momentum, minus the Lagrangian.  Representing the sum of all kinetic and potential energies of the aforementioned dynamic system, FTP, identify this function named for the Irish mathematician who discovered it.
It was originally introduced to express the rate of change in time of the condition of a dynamic physical system - one regarded as a set of moving particles.  
Hamiltonian function