P.p. of → generalize
Fr.: coordonnées généralisées
In a material system, the independent parameters which completely specify the configuration of the system, i.e. the position of its particles with respect to the frame of reference. Usually each coordinate is designated by the letter q with a numerical subscript. A set of generalized coordinates would be written as q1, q2, ..., qn. Thus a particle moving in a plane may be described by two coordinates q1, q2, which may in special cases be the → Cartesian coordinates x, y, or the → polar coordinates r, θ, or any other suitable pair of coordinates. A particle moving in a space is located by three coordinates, which may be Cartesian coordinates x, y, z, or → spherical coordinates r, θ, φ, or in general q1, q2, q3. The generalized coordinates are normally a "minimal set" of coordinates. For example, in Cartesian coordinates the simple pendulum requires two coordinates (x and y), but in polar coordinates only one coordinate (θ) is required. So θ is the appropriate generalized coordinate for the pendulum problem.
Fr.: forces généralisées
In → Lagrangian dynamics, forces related to → generalized coordinates. For any system with n generalized coordinates qi (i = 1, ..., n), generalized forces are expressed by Fi = ∂L/∂qi, where L is the → Lagrangian function.
Fr.: quantité de mouvement généralisée
In → Lagrangian dynamics, momenta related to → generalized coordinates. For any system with n generalized coordinates qi (i = 1, ..., n), generalized momenta are expressed by pi = ∂L/∂q.i, where L is the → Lagrangian function.
Fr.: vitesses généralisées