text: A type 4 generating function for a canonical transformation is a function of time and this quantity before and after the transformation.
full_question: A type 4 generating function for a canonical transformation is a function of time and this quantity before and after the transformation. Hamilton's characteristic function generates a transformation in which all values of this quantity become constants of the motion. For a charged particle moving in a magnetic field, the classical value for this quantity in absence of the field, plus the product of the particle's charge and the magnetic vector potential, gives its "canonical" value. A coordinate is "cyclic" if the coordinate's canonically conjugate value for the generalized form of quantity is conservedthis is the case for any generalized coordinate Q because it equals the partial derivative of the Lagrangian with respect to the generalized velocity Q-dot. It is said to be "conjugate" to position, since it is equal to the Fourier transform of position. For 10 points, name this quantity that, in Newtonian mechanics, is conserved in both inelastic and elastic collisions.
first_sentence: A type 4 generating function for a canonical transformation is a function of time and this quantity before and after the transformation.
raw_answer: linear momentum [or generalized momentum; or canonical momentum; or conjugate momentum; do not accept "angular momentum"]