Ehrenfest's famous Principle of Adiabatic Invariance states that the ratio of the energy of an oscillatory motion to the frequency stays constant. This principle can be demonstrated with a simple pendulum. Consider a simple pendulum executing small-amplitude oscillations. The string with negligible mass is shortened an amount Al very slowly, so that the change in amplitude from one oscillation to the next is negligible. Show that under these conditions, the ratio of the energy to the frequency remains constant.

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero. 

Well it depends on the object or substance