1.We consider a free particle of Lagrangian L = m ˙ x2/2. Calculate the action along the physical trajectory in terms of the positions and times of departure (x1, t1)

and arrival (x2, t2).

2.Consider a harmonic oscillator L = (m/2)( ˙ x2 − ω2x2). Calculate the action, setting T = t2 − t1.

3.Calculate the action for a constant force L = m ˙ x2/2 − Fx.

4.Show that the momentum at the point of arrival x2 is given by

5.Show that the energy E = p ˙ x − L at the point of arrival x2 is given by

Transcribed Image Text:

P2 X=X2 S12 32