Lagrange's equations look funny at first, but they should make sense in ordinary cases. to see that this is so: (a) write down the lagrangian for a particle moving near the surface of the earth, in three dimensions, subject only to the force of gravity. (b) derive lagrange's equations of motion for this case, and show that they are the usual equations of motion you would expect.

Because its reliable.   there is no pollution  the chances of a radiation leak is low

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.