Center of Mass Motion

The Grand Jete. Illusion of Floating.

last updated on 7 May/97


 

While the center of mass motion of a body in a gravitational field is a parabola in y-x and also y-t space, one can create an illusion of floating. This means that the body seems to be suspended in space and time at a height.

A premier example of this is the dancer Paquita executing the Grand Jete where the purpose is to create the illusion of floating.

The dancer, Paquita, of the American Ballet Theatre. The dots are the digitization points of the dancer's head. In the following graphs, the displacement, velocity and acceleration axese have not been calibrated so please read them only for qualitative information. Zero does mean zero, though.


The dancer, Pauita, at the top of her arc. Notice that the raising of her legs had changed her cm to a much higher position RELATIVE to her head.

The y-t curve of the dancer's head. Note that it is , indeed, flattened on top!! It floats!

velocity-time curve of the dancer's head. After the dancer has launched herself, the velocity decreases but there is a flattening of this curve at t = 0.4 sec. She floats!

The acceleration -time curve. At t=0.4 sec, the acceleration is approximately zero. Again, the head floats.