Computer-Aided Analysis of Mechanical Systems by Parviz E. Nikravesh

By Parviz E. Nikravesh

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The term coordinates can refer to any of the commonly used coordinate systems, but it can also refer to any of an infinite variety of other sets of parameters that serve to specify the configuration of a system. Vectors of coordinates are designated in this text by column vectors q [q" q2" .. ,qnf, where n is the total number of coordinates used in describing the system. Examples of commonly used coordinates are Lagrangian and Cartesian coordinates. In this text, Cartesian coordinates are used almost exclusively.

66) dt dt dt Thus, for vectors that are written in terms of their components in a fixed Cartesian coordinate system, the second time derivative may be calculated in terms of the second time derivatives of the components of the vector. Just as in the differentiation of a vector function, the derivative of a matrix whose components depend on a variable t may be defined. Consider a matrix A(t) [aa(f)]. 4 If a is a nonzero time-dependent 3-vector, A = [a, a] is a 3 X 4 matrix, and C = AAT , what is the condition on a for which C will be a null matrix?

The input data describing this system must contain such information as: 1. 2. 3. 4. 5. 6. 7. 8. ~e,~L@Lbedescribed­ Jhis information is needed only if a graphical display of the system is required. The minimum requirement for generating and communicating a set of input data to the analysis program is an alphanumeric computer terminaL The input can be entered manually via the keyboard and transmitted to the analysis program, which may reside on a mainframe computer, a minicomputer, or a personal microcomputer.

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