“centre of mass”的概念、定义、翻译、参考文献-科学参考

centre of mass

Physics

The point at which the whole mass of a body may be considered to be concentrated. This is the same as the centre of gravity, the point at which the whole weight of a body may be considered to act, if the body is situated in a uniform gravitational field.

Mathematics

Suppose that particles P₁,…, P_n, with corresponding masses m₁,…, m_n, have position vectors r₁,…, r_n, respectively. The centre of mass (or centroid) is the point with position vector r_C, given by

$m r_{C} = \sum_{i = 1}^{n} m_{i} r_{i}, where m = \sum_{i = 1}^{n} m_{i},$

m being the total mass of the particles.

For a rigid body, the corresponding definitions involve integrals. In vector form, the position vector r_C of the centre of mass is given by

$m r_{C} = \int_{R}^{} ρ (r) r d V where m = \int_{R}^{} ρ (r) d V .$

where ρ‎(r) is the density at the point with position vector r, R is the region occupied by the body and m is the total mass of the body.

Astronomy

The point in a body or system of bodies which acts as if all the mass were concentrated there; also known as centre of inertia. The gravitational force between two massive bodies acts along the line joining their centres of mass. For a sphere of uniform density, or a sphere whose density varies radially from the centre, the centre of mass is at the centre of the sphere. In a uniform gravitational field, a body’s centre coincides with its centre of gravity.

单词	centre of mass
释义	centre of mass Physics The point at which the whole mass of a body may be considered to be concentrated. This is the same as the centre of gravity, the point at which the whole weight of a body may be considered to act, if the body is situated in a uniform gravitational field. Mathematics Suppose that particles P₁,…, P_n, with corresponding masses m₁,…, m_n, have position vectors r₁,…, r_n, respectively. The centre of mass (or centroid) is the point with position vector r_C, given by $m r_{C} = \sum_{i = 1}^{n} m_{i} r_{i}, where m = \sum_{i = 1}^{n} m_{i},$ m being the total mass of the particles. For a rigid body, the corresponding definitions involve integrals. In vector form, the position vector r_C of the centre of mass is given by $m r_{C} = \int_{R}^{} ρ (r) r d V where m = \int_{R}^{} ρ (r) d V .$ where ρ‎(r) is the density at the point with position vector r, R is the region occupied by the body and m is the total mass of the body. Astronomy The point in a body or system of bodies which acts as if all the mass were concentrated there; also known as centre of inertia. The gravitational force between two massive bodies acts along the line joining their centres of mass. For a sphere of uniform density, or a sphere whose density varies radially from the centre, the centre of mass is at the centre of the sphere. In a uniform gravitational field, a body’s centre coincides with its centre of gravity.
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