“rigid body”的概念、定义、翻译、参考文献-科学参考

rigid body

Physics

A body in which the distances between the particles that make up the body are always constant. This means that a rigid body cannot be compressed or deformed. The concept of a rigid body is a mathematical idealization but is a very useful approximation that gives a good description of many systems in both Newtonian mechanics and quantum mechanics. The concept is not valid in the special theory of relativity because it does not satisfy the invariance requirements of the Lorentz group; however, for bodies that are moving much slower than the speed of light this is not a serious problem.

Mathematics

An object with the property that it does not change shape whatever forces are applied to it. It is used in a mathematical model to represent an object in the real world. It may be a system of particles held in a rigid formation, or it may be a distribution of mass in the form of a rod, a lamina, or some 3-dimensional shape. In general, a rigid body has six degrees of freedom—three to determine the body’s centre of mass and three more to specify the body’s orientation about its centre of mass. The equations of motion for a rigid body are

$m \frac{d^{2} r_{G}}{d t^{2}} = \sum F_{k}, \frac{d L_{G}}{d t} = \sum r_{k} \times F_{k},$

where m denotes the mass of the body, r_G is the position vector of the centre of mass, L_G is the angular momentum about the centre of mass, F_k are the external forces acting on the body, and r_k × F_k is the moment of the force F_k (so that r_k is the position vector of a point on the line of action of the force F_k). See also inertia tensor.

单词	rigid body
释义	rigid body Physics A body in which the distances between the particles that make up the body are always constant. This means that a rigid body cannot be compressed or deformed. The concept of a rigid body is a mathematical idealization but is a very useful approximation that gives a good description of many systems in both Newtonian mechanics and quantum mechanics. The concept is not valid in the special theory of relativity because it does not satisfy the invariance requirements of the Lorentz group; however, for bodies that are moving much slower than the speed of light this is not a serious problem. Mathematics An object with the property that it does not change shape whatever forces are applied to it. It is used in a mathematical model to represent an object in the real world. It may be a system of particles held in a rigid formation, or it may be a distribution of mass in the form of a rod, a lamina, or some 3-dimensional shape. In general, a rigid body has six degrees of freedom—three to determine the body’s centre of mass and three more to specify the body’s orientation about its centre of mass. The equations of motion for a rigid body are $m \frac{d^{2} r_{G}}{d t^{2}} = \sum F_{k}, \frac{d L_{G}}{d t} = \sum r_{k} \times F_{k},$ where m denotes the mass of the body, r_G is the position vector of the centre of mass, L_G is the angular momentum about the centre of mass, F_k are the external forces acting on the body, and r_k × F_k is the moment of the force F_k (so that r_k is the position vector of a point on the line of action of the force F_k). See also inertia tensor.
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