Abstract
As we mentioned in Chapter 1, our intention is to describe the dynamic equations of rigid body motion by using Cartesian tensors. Cartesian tensor analysis, being more general than vector analysis, is powerful and, if properly used, can result in a tensor formulation for the equations of general motion of a dynamic system. As we shall show in Chapter 5, such a formulation will enable us to derive computationally efficient algorithms for the dynamic equations of motion of rigid-link open-chain robot manipulators. In this chapter, we provide an introduction to the theory of Cartesian tensors. Moreover, based on 1-1 operators between three dimensional vectors and second order skew-symmetric Cartesian tensors, this theory is extended here by establishing a number of tensor-vector identities. These identities, as we shall see in the following chapters, will allow for easy algebraic manipulations of the equations of motion of a complex dynamic system such as those of a robotic system
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Balafoutis, C.A., Patel, R.V. (1991). Cartesian Tensor Analysis. In: Dynamic Analysis of Robot Manipulators. The Springer International Series in Engineering and Computer Science, vol 131. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3952-0_3
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DOI: https://doi.org/10.1007/978-1-4615-3952-0_3
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