Stress_Balance_Principles_02_The_Momentum_Principles -...

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Section 3.2 Solid Mechanics Part III Kelly 327 3.2 The Momentum Principles In Parts I and II, the basic dynamics principles used were Newton’s Laws, and these are equivalent to force equilibrium and moment equilibrium. For example, they were used to derive the stress transformation equations in Part I, §3.4 and the Equations of Motion in Part II, §1.1. Newton’s laws there were applied to differential material elements. An alternative but completely equivalent set of dynamics laws are Euler’s Laws ; these are more appropriate for finite-sized collections of moving particles, and can be used to express the force and moment equilibrium in terms of integrals. Euler’s Laws are also called the Momentum Principles : the principle of linear momentum (Euler’s first law) and the principle of angular momentum (Euler’s second law). 3.2.1 The Principle of Linear Momentum Momentum is a measure of the tendency of an object to keep moving once it is set in motion. Consider first the particle of rigid body dynamics: the (linear) momentum p is defined to be its mass times velocity, v p m = . The rate of change of momentum p is a v v p m dt
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 3 taught by Professor Staff during the Fall '11 term at Auckland.

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Stress_Balance_Principles_02_The_Momentum_Principles -...

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