relative_absolute

# relative_absolute - Relative and Absolute Coordinates in...

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Relative and Absolute Coordinates in Energy Expressions There are two important principles to remember when writing down kinetic and potential energy expressions: 1. The expression for kinetic energy MUST be based on speeds that are found from absolute velocity vectors; that is, with respect to fixed reference frames. The reason for this requirement is that the work energy equation is derived from Newton’s 2 nd Law, F = ma , where a is the acceleration as seen by a fixed observer . 2. The expression for potential energy in a spring is dependent on the relative motion between the two ends of the spring. These issues become relevant to you when you write down the kinetic and potential energy expressions for Lagrange’s equations. To help make these points,let’s consider (for simplicity) a simple chain system of springs and masses. If you use absolute coordinates, then the speed of each mass (as seen by a fixed observer) is ˙ x j since the coordinates x j are measured from fixed reference lines. The stretch in the spring between particles 2 and 3 is given

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