Lagrange's equations

Lagrange's equations

Equations of motion of a mechanical system for which a classical (non-quantum-mechanical) description is suitable, and which relate the kinetic energy of the system to the generalized coordinates, the generalized forces, and the time. If the configuration of the system is specified by giving the values of f independent quantities q1,…, qf, there are f such equations of motion.

In their usual form, these equations are equivalent to Newton's second law of motion and are differential equations of the second order for the q's as functions of the time t.

Lagrange's equations

[lə′grän·jəz i‚kwā·zhənz]
(mechanics)
Equations of motion of a mechanical system for which a classical (non-quantum-mechanical) description is suitable, and which relate the kinetic energy of the system to the generalized coordinates, the generalized forces, and the time. Also known as Lagrangian equations of motion.
References in periodicals archive ?
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.
Lagrange's equations related to the fixed system OXYZ, taking into account the generalized coordinated: radius p and rotational angle [section] can be written as follows to get the equation governing the movement in radial direction (see eq.
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).
Next, Lagrange's equations are derived and their integration is discussed.

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