The equations of motion are derived using

Lagrange's equation and are considered as a nonlinear system of second-order differential equations.

According to

Lagrange's equation, dynamic equation of the beam element can be written as

and from

Lagrange's equation of motion and equation (4.4) it can be shown that

Lagrange's equation with multipliers has been used to write the equation of movement, together with the nonholonomic couplings leading to a system with 1+s equations having 1+s unknowns: [q.sub.1], ..., [q.sub.s]; [[lambda].sub.1], ..., [[lambda].sub.s].

The pre-mentioned differential formulation of the equations of motion is equivalent to integral formulation, which requires the application of

Lagrange's equation of motion.

The only strict prerequisite is a working knowledge of intermediate undergraduate dynamics, but some familiarity with simple aspects of

Lagrange's equation would also be helpful.

Therefore, the equations were formulated with generalized coordinates according to the general process of

Lagrange's equation of motion.

The governing equation of the inverted pendulum model can be derived by using

Lagrange's equations. The positions of the lump mass m and the cart are written as

For this edition they have added 59 new problems, and a new chapter on applying

Lagrange's equations to deriving equations of motion.

Organized according to the steps in a control design project, the text first discusses kinematic and dynamic modeling methods, including programmed constraints,

Lagrange's equations, Boltzmann-Hamel equations, and generalized programmed motion equations.

Firstly, the dynamic model of the flexible links mounted with multiple PZT transducers is formulated using

Lagrange's equations and AMM, and the experimental modal tests of the flexible links are implemented to verify the assumed mode shapes.

Using

Lagrange's equations of the second kind (Ripianu, 1977), the differential equations for the TRT1 and RTT robots with three degrees of freedom were deduced, expressed by the equations (1) and (2).