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I have the following problem related to my thesis which is a 3dof mechanical system. In this system, there are two masses ($m_1,m_2$) that are linked with weightless two links ($l_1,l_2$). Two joints have consisted of spring-damper systems which can be rotated around the y-axis ($\theta_1,\theta_2$). The total system can be rotated around the x-axis ($\omega$) at the point of the origin of the cartesian plane. In order to derive the dynamic equation for the system, how can I obtain the potential and kinetic energies?

3-dof mechanical system

Piyumal Samarathunga
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  • I would look up double pendula. You should find results that will make it clear how to do your problem. – Cameron Williams Nov 01 '19 at 11:59
  • Could you show us your efforts to solve it? – Cesareo Nov 01 '19 at 12:03
  • #Cameron Williams I also thought about the double pendulum (but it is 2dof). But the problem is that the system is rotating around the x-axis, then it behaves like an articulated robot arm as I guess (hence it is 3dof). So it is a little bit confusing to write the expressions for the kinetic and potential energies. – Piyumal Samarathunga Nov 01 '19 at 12:47
  • #Cesareo

    I could write, (by considering the coordinates of $m_1$ is $(x_1,y_1)$ and the coordinates of $m_2$ is $(x_2,y_2)$)

    P.E: $ V = m_1 g y_1 + m_2 g y_2 + \frac{1}{2} k_1 \theta_1^2 + \frac{1}{2} k_2 (\theta_2 - \theta_1)^2$

    K.E: $ T = \frac{1}{2} m_1 (\dot x_1^2 + \dot y_1^2) + \frac{1}{2} (\dot x_2^2 + \dot y_2^2) $

    But I can't figure out how to enter the rotation of the system around the x-axis with $\omega$ for the kinetic and potential energies.

     – Piyumal Samarathunga Nov 01 '19 at 13:32

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