Note that "x" has an explicit dependence on time, whilst "V" does not; consequently::formula_90so we can set:formula_91Then,: formula_92The right hand side is the energy, and Noether's theorem states that formula_93 (i.e.
) Note that "x" has an explicit dependence on time, whilst "V" does not; consequently:: formula_124so we can set: formula_125Then,The right hand side is the energy and Noether’s theorem states that formula_126 (i.e.