Generalized Dynamics: Kane’s Equations and Lagrange’s Equations

In this chapter, we apply the procedures developed in Chapter 11 to obtain governing dynamical equations of motion. We will consider two approaches: the use of Kane’s equations and the use of Lagrange’s equations. We will discover that these approaches are related. Indeed, we will use Kane’s equations to develop Lagrange’s equations. We will illustrate and compare the use of Kane’s and Lagrange’s equations by obtaining equations of motion for the various examples considered in Chapter 11. In addition, we will also consider the triple-bar pendulum and the

N

-bar pendulum (an

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-bar pendulum may be considered as a model of a chain or cable).