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Recall from Chap. 1 that one of the best-known equations in science is F = ma, which was put forth by Sir I. Newton as his second law of motion. This equation asserts that relative to an inertial frame of reference, the (time) rate of change of the linear momentum mv of a particle of mass m must balance the sum of all forces F that act on the particle. For this reason, this law of motion (actually postulate) is also called balance of linear momentum. Whereas Newton considered only individual mass points (like the moon or an apple), among others, L. Euler showed that many bodies can be treated as a continuous collection of mass points (i.e., a continuum), each particle of which must obey Newton’s second law. Indeed, as it turns out, three basic postulates provide the equations of motion for any continua:

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Fundamental Balance Relations

  • 章节

  • 发表日期：

    2025年

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  • Jay D. Humphrey,
  • Sherry L. O’Rourke

摘要

Recall from Chap. 1 that one of the best-known equations in science is F = ma, which was put forth by Sir I. Newton as his second law of motion. This equation asserts that relative to an inertial frame of reference, the (time) rate of change of the linear momentum mv of a particle of mass m must balance the sum of all forces F that act on the particle. For this reason, this law of motion (actually postulate) is also called balance of linear momentum. Whereas Newton considered only individual mass points (like the moon or an apple), among others, L. Euler showed that many bodies can be treated as a continuous collection of mass points (i.e., a continuum), each particle of which must obey Newton’s second law. Indeed, as it turns out, three basic postulates provide the equations of motion for any continua: