Arope of length l is thrown over two small frictionless pulleys separated by distance d (pulleys are placed at the same height). two masses, m1 and m2, are attached to the ends of the rope. each of two masses can oscillate in the plane of the system while rope is allowed to slide. write down lagrangian and euler-largrange equations for this system.

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. 

Because they're in different places for this the temperature varies.

connectedness in handwriting analysis is a useful tool in establishing the writer’s method of thinking and its perception in where he/she fits in to the environment around him in the social sense. in addition, the more connected the writing of an individual, the more he/she is flexible and single minded.