Four particles are directed upward in a uniform gravitational field with the following initial conditions. Show by

Question:

Four particles are directed upward in a uniform gravitational field with the following initial conditions.

(1) z(0) = z0 p.(0) = p.(0) = p.(0) = p + Apo P.(0) = po + ApO (2) z(0) = 20 + Az: (3) z(0) = zoi (4) z(0) = z, + Azo: %

(1) z(0) = z0 p.(0) = p.(0) = p.(0) = p + Apo P.(0) = po + ApO (2) z(0) = 20 + Az: (3) z(0) = zoi (4) z(0) = z, + Azo: %

Show by direct calculation that the representative points corresponding to these particles always define and area in phase space equal to ∆z0 ∆ P0. Sketch the phase paths, and show for several times t > 0 the shape of the region whose area remains constant.