Transcription of Single and Double plane pendulum - LSU
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Single and Double plane pendulum - LSU
Single and Double plane pendulumGabriela Gonz alez1 IntroductionWe will write down equations of motion for a Single and a Double plane pendulum , followingNewton s equations, and using Lagrange s 1: A simple plane pendulum (left) and a Double pendulum (right). Also shown arefree body diagrams for the forces on each Newton s equationsThe Double pendulum consists of two massesm1andm2, connected by rigid weightlessrods of lengthl1andl2, subject to gravity forces, and constrained by the hinges in the rodsto move in a plane . We choose a coordinate system with the origin at the top suspension1point, the x-axis as a horizontal axis in the plane of motion, and the y-axis pointing down(so that gravity forces have positive components). The Single plane pendulum , a simplercase, has a Single particle hanging from a rigid ConstraintsThe simple pendulum system has a Single particle with position vectorr= (x,y,z).
for the problem. 2.3.2 Double Pendulum In the double pendulum, Newton’s second law on each particle is F i = m i¨r i: m 1¨r 1 = − T 1 l 1 r 1 + T 2 l 2 (r 2 −r 1)+m 1g …
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