By Donald T. Greenwood
Emphasizing studying via challenge fixing, Donald Greenwood analyzes intimately the strengths and weaknesses of varied techniques to dynamics. He describes concepts that might increase computational potency significantly, in particular whilst utilized to advanced dynamical platforms. A key function of his textual content is the inclusion of many confirmed examples and homework difficulties. The publication is meant to be used in graduate classes on dynamics and may entice training mechanical and aerospace engineers.
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An ideal constraint is a workless constraint which may be either scleronomic or rheonomic. 229). Examples of ideal constraints include frictionless constraint surfaces, or rolling contact without slipping, or a rigid massless rod connecting two particles. Another example is a knife-edge constraint that allows motion in the direction of the knife edge without friction, but does not allow motion perpendicular to the knife edge. Ideal constraint forces, such as the internal forces in a rigid body, may do work on individual particles due to a virtual displacement, but no work is done on the system as a whole because these forces occur in equal, opposite and collinear pairs.
103) i=1 where ρi is the position vector of the ith particle relative to the center of mass. 104) j=1 Now take the vector product of ρi with both sides of this equation and sum over i. 106) i=1 for a reference point at the center of mass. 107) i=1 j=1 because the internal forces fi j occur in equal, opposite, and collinear pairs. 109) where Mc is the external applied moment about the center of mass. 110) applies in each of two cases: (1) the reference point is ﬁxed in an inertial frame; or (2) the reference point is at the center of mass.
127) i=1 We see that the total kinetic energy is the sum of three parts: (1) the kinetic energy due to the total mass moving at the speed of the reference point; (2) the kinetic energy due to motion relative to the reference point; and (3) the scalar product of the reference point velocity and the linear momentum of the system relative to the reference point. 127) is an important and useful result. It is particularly convenient in the analysis of systems having a reference point whose motion is known but which is not at the center of mass.
Advanced Dynamics by Donald T. Greenwood