## Introduction to dynamics and controlAn integrated presentation of dynamics, vibrations, and control theory, emphasizing the fundamentals of dynamics. The text's flexible structure makes it useful for integrated courses covering all three areas, individual courses in dynamics, and as a quick refresher for professionals. Includes examples, problems and applications. |

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angular momentum angular velocity assume asymptotically axes characteristic equation coefficients conclude considering Eq constant coordinates d'Alembert's principle damped systems defined Denoting Determine differential equation discrete-time dynamics eigenvalue problem equations of motion equilibrium point expressed FIGURE frame xyz free-body diagram frequency response given by Eq Hence impulse response inertia initial conditions input Inserting Eqs Introducing Eq Introducing the notation kinetic energy known Lagrange's equations Laplace transform Let us consider linear momentum linear system magnitude mass center modal vectors Moreover natural frequency Newton's second law nonlinear Nyquist plot obtain orbit orthogonality parameters phase angle phase plane plot poles position potential energy relative represents rigid body root loci rotation s-plane second-order system shown in Fig side of Eq simply solution of Eq stability step response system of Fig system of particles system of Problem undamped unit step function unit vectors velocity vector virtual displacements write zero