英语词汇“generalized coordinate”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

generalized coordinate n. Mathematics each of a general set of coordinates defining the state of a system, usually chosen so that the number of coordinates equals the number of degrees of freedom of the system; usually in plural.Generalized coordinates are used esp. where the number of degrees of freedom is smaller than the number of standard Cartesian coordinates required to define the state of the system. For example, a body constrained to move on a sphere requires three Cartesian coordinates (for the three dimensions of space) but only two generalized coordinates (longitude and latitude).

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1865 P. G. Tait & W. J. Steele Dynamics of Particle (ed. 2) 346 D'Alembert's Principle supplies us with a far simpler mode of investigating the motions of any system of free or connected particles: especially when it is simplified in its application by the beautiful system of Generalized Co-ordinates introduced by Lagrange.

1955 Math. Mag. 28 270 Any polar point (r, θ) has generalized coordinates (−1)ⁿr, θ + nπ.

2007 U. Krey & A.Owen Basic Theoret. Physics viii. 49 Often p_i has the physical dimension of angular momentum, in the case where the corresponding generalized coordinate is an angle.

单词	generalized coordinate
释义	> as lemmas generalized coordinate generalized coordinate n. Mathematics each of a general set of coordinates defining the state of a system, usually chosen so that the number of coordinates equals the number of degrees of freedom of the system; usually in plural.Generalized coordinates are used esp. where the number of degrees of freedom is smaller than the number of standard Cartesian coordinates required to define the state of the system. For example, a body constrained to move on a sphere requires three Cartesian coordinates (for the three dimensions of space) but only two generalized coordinates (longitude and latitude). ΚΠ 1865 P. G. Tait & W. J. Steele Dynamics of Particle (ed. 2) 346 D'Alembert's Principle supplies us with a far simpler mode of investigating the motions of any system of free or connected particles: especially when it is simplified in its application by the beautiful system of Generalized Co-ordinates introduced by Lagrange. 1955 Math. Mag. 28 270 Any polar point (r, θ) has generalized coordinates (−1)ⁿr, θ + nπ. 2007 U. Krey & A.Owen Basic Theoret. Physics viii. 49 Often p_i has the physical dimension of angular momentum, in the case where the corresponding generalized coordinate is an angle. extracted from generalizedadj. < as lemmas
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