# Double pendulum Calculations

A double pendulum consists of a pendulum of mass m2 hanging from a pendulum of mass m1. The motion of both parts of the double pendulum is constrained to the x-y plane. Both strings are "unstretchable" and having length I2 and I1, respectively.

a) How many degrees of freedom does this system have?

Using the variable theta1 and theta2 for the angles the strings make with the vertical, write expressions for

b) the kinetic energy

c) the potential energy

d) Write the equations of motion for the system in terms in theta1 and theta 2, and their time derivatives.

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#### Solution Summary

The solution determines the kinetic and potential energy.

Lagrange's Equation for a double pendulum

A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lengths of rigid, massless, rod and bobs of equal mass and if both pendula are confined to move in the same plane find Lagrange's equation of motion for the system...Do NOT assume small angles.

Please include diagram and complete, clear explanation.

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