Download e-book for kindle: Mathematical Principles of Mechanics and Electromagnetism: by Chao-cheng Wang

By Chao-cheng Wang

ISBN-10: 1468435361

ISBN-13: 9781468435368

ISBN-10: 1468435388

ISBN-13: 9781468435382

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Extra info for Mathematical Principles of Mechanics and Electromagnetism: Part A: Analytical and Continuum Mechanics

Sample text

R Newton's First Law. There exists a particular frame of reference, called an inertial frame, relative to which the linear momentum of a particle remains constant when the force acting on the particle vanishes. As remarked before, the condition that force vanishes is independent of the choice of the frame. Consequently, the condition that linear momentum remains constant under vanishing force can be used as a criterion for an inertial frame, and Newton's first law merely asserts the existence of such a frame.

Sec. 5) may be interpreted in the following way: For a fixed time to and position qo E Lto we call any smooth curve q(r) E Lto passing through qo a virtual displacement from qo. Since q(r) is required to stay in L to, we say that the virtual displacement is consistent with the constraint. 5) is satisfied at q = qo and at t = to if and only if the total power of the constraint forces and the constraint moments vanishes identically at the point qo in all virtual displacements from qo. The truth of this claim is more or less obvious.

We can regard t as the generalized coordinate qn+l on vi!. Then a motion of (f! II having the special coordinate form r qn+l = t. 12), respectively, when the summation on Ll is extended to (n 1). 16) except that Ll, r are summed from 1 to (n + 1). + Sec. 4 Lagrangian Mechanics of Particles and Rigid Bodies 23 4. Dynamical Principles for Particles and Rigid Bodies In the preceding three sections we have considered motions in general for particles and rigid bodies. In classical mechanics motions of particles and rigid bodies are regarded as results caused by forces and moments and are governed by certain principles of dynamics.

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Mathematical Principles of Mechanics and Electromagnetism: Part A: Analytical and Continuum Mechanics by Chao-cheng Wang

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