PHY.7:2 - Problem

Writing L=T-V and applying the Euler-Lagrange formula leaves important physical work hidden. Which interactions are represented by the potential? Does a moving support contribute to the velocity? Which endpoint quantities are fixed? Can the constraint really be imposed on every varied history?

These choices can change the resulting motion. A missing velocity-dependent interaction can leave the energy apparently reasonable while removing a force. Discarding a boundary term can replace a loaded boundary by a free one. Extending a rule for position constraints to a different kind of constraint can select a different evolution.