One method starts with a choice for the total energy , E.

Once E is selected, find a value of x for which V(x) = E. (call that value x

_{0})Then since p = ± √2m sqrt( E - V(x)), a first point on the phase plot (p,x) is (0, x

_{0})Since the argument of the square root cannot be allowed to be negative, the next points the next x value must be

either to the left or right of x

_{0}and there will be two corresponding p values (± something)This process can be continued to get additional points.

Selecting different values of E will generate a family of trajectories.

Of course there might be more than one value of x for which V(x) = E. Generally the trajectories started from different

such points will join up. A good example of this is the simple harmonic oscillator.

Richard P.

tutor

The expression phase plane normally means a plot of momentum (p) vs position (x).

For one conservative one dimensional problems one has the relation

E = p^2 /2m + V(x) , were m is the mass of the particle and E is the total conserved energy,

This equation can be considered an implicit relation between p and x (parameterized by E)

Thus for a given E, the equation determines a curve in the plane.

It is possible that the expression phase plane is being used in some other context unknown to me.,

Report

04/03/18

Ashley H.

04/03/18