- #1

mathmari

Gold Member

MHB

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I am looking at the following:

Find the energy function for the double pendulum, with vertical constant and uniform gravity field

- for motion restricted at vertical plane
- for motion in space

The potential energy of the system is given by $PE=m_1gy_1+m_2gy_2$.

The kinetic energy is given by $KE=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$.

Therefore, the energy function is equal to $$E=PE+KE=m_1gy_1+m_2gy_2+\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$$ Is this correct?

How can we distinct between motion restricted at vertical plane and motion in space? And what does a uniform gravitational field imply?

(Wondering)