Analytical Elements Of Mechanics

Analytical Elements of Mechanics, Volume 1, is the first of two volumes intended for use in courses in classical mechanics. The books aim to provide students and teachers with a text consistent in content and format with the author’s ideas regarding the subject matter and teaching of mechanics, and to disseminate these ideas. The book opens with a detailed exposition of vector algebra, and no prior knowledge of this subject is required. This is followed by a chapter on the topic of mass centers, which is presented as a logical extension of concepts introduced in connection with centroids. A theory of moments and couples is constructed without reference to forces, these being mentioned only in illustrative examples. This is done because it eventually becomes necessary to apply the theory to systems of vectors which are not forces, such as momenta and impulses. Equilibrium is discussed in the final chapter, preceded by extended examination of the concept of force.

Analytical Elements of Mechanics, Volume 2: Dynamics focuses on the processes, methodologies, approaches, and technologies involved in classical mechanics. The book first offers information on the differentiation of vectors, including vector functions of a scalar variable; derivatives of sums and products; vector tangents of a space curve; vector binormals of a space curve; and Taylor's theorem for vector functions. The manuscript then ponders on kinematics, as well as angular velocity and acceleration, absolute and relative velocity and acceleration, and rates of change of orientation of a rigid body. The text examines second moments and laws of motion. Discussions focus on second moments of sets of particles and continuous bodies, second moments of a point, motions of rigid bodies, and linear and angular momentum. The publication is a dependable reference for readers interested in the dynamics of the analytical elements of mechanics.