First, to make sure i have this right, lagrangian mechanics, when describing a dynamic system, is the time derivative of the positional partial derivatives (position and velocity) of the lagrangian of the system, which is the difference between the kinetic and potential energy of the system. (set equal to external forces on the system, Q) L = T-U is this right? So my question is: is the definition of a lagrangian, T-U, valid only for constant mass systems or can it still be used for variable mass systems? what about the derivatives of the lagrangian, would i need to find the partial derivative of the lagrangian with respect to mass? and finally, im assuming the answers to these questions are very different if we are talking about a time varying mass vs a mass that varies with postion, yes? Any help would be much appreciated. As im sure you can tell, i am very lost at the moment As background for what im working on, it's a mass on a spring (assuming attached to a rigid/ non-moving body, so for now 1 degree of freedom) with the mass decresing with respect to time. Finally as the mass decreases there is a perodic downward force applied to the mass decreasing in amplitude proportional to the decrease in mass.