Choosing our generalized coordinates as the horizontal ...

The angular velocity of the pendulum is simply (2.10) Substituting Equations 2.9 and 2.10 into Equation 2.7 yields (2.11) which, upon simplifying, becomes (2.12) The total kinetic coenergy is (2.13) Since the cart moves only in the horizontal direction, the potential energy of the system is determined entirely by the angle of the pendulum ... ................
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