An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 5 Search : generalized
generalized
  هروینیده   
harvinidé

Fr.: généralisé   

Made general. → generalized coordinates; → generalized velocities.

P.p. of → generalize

generalized coordinates
  هماراهای ِ هروینیده   
hamârâhâ-ye harvinidé

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.

generalized; → coordinate.

generalized forces
  نیروهای ِ هروینیده   
niruhâ-ye harvinidé

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.

generalized; → force.

generalized momenta
  جنباک‌های ِ هروینیده   
jonbâkhâ-ye harvinidé

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.

generalized; → momentum.

generalized velocities
  تنداهای ِ هروینیده   
tondâhâ-ye harvinidé

Fr.: vitesses généralisées   

The time → derivatives of the → generalized coordinates of a system.

generalized; → velocity.