## Two degrees of freedom

Consider the two degrees of freedom (2-DOF) system shown in Fig. G.4. The system consists of three rigid bodies connected by two ideal torsional springs Czi and Cz3 that model the elastic properties in bending direction. The damping is modeled by two viscous dampers, Keq\2 and Keq23 respectively. The input is the force F and the output is the displacement of the point action of F. Gravity is completely neglected.

The equations of motion of the above (2-DOF) system can be solved more easily using Lagrange's equations than using Newton's law directly as in Section G.1. The

Figure G.4: Two degrees of freedom system (superelement) of length Lse consisting of three rigid bodies with lengths 2(1 — —3) • Lse, —3 • Lse, and 2(1 — —3) • Lse.

Lagrange formulation states that the equations of motion can be derived from d ( dT \ ( dT \ ( dU \

where qi = dqi/dt is the generalized velocity, T is the kinetic energy of the system, U the potential energy of the system, an Qi represents all the nonconservative forces corresponding to qi. Here d/dqi denotes the partial derivative with respect to the coordinate qi. For conservative systems, Qi = 0 and Eq. (G.15) reduces to

## Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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