Titlebook: Classical Mechanics with Mathematica®; Romano Antonio Textbook 20121st edition Springer Science+Business Media New York 2012 Lagrangian an

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Tensor AlgebraThis chapter contains an introduction to tensor algebra. After defining covectors and dual bases, the space of covariant two-tensor is introduced. Then, the results derived for this space are extended to the general space of the (.,.)-tensors.

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Duality and Euclidean TensorsIn this section, we show that when .. is a Euclidean vector space, there is an isomorphism among the tensor spaces ...(..) for which .+. has a given value. In other words, we show the existence of an isomorphism between .. and ..., of isomorphisms between ..., ..., and ..., and so on.

WAG

Differentiable ManifoldsLet . be an open set of ... The real-valued function . :.→. is said to be of...(.) or a ... in ., where .≥0, if it is continuous with its partial derivatives up to the order .. In particular, a .. function in . is a continuous one.

CLAY

One-Parameter Groups of DiffeomorphismsA.. on a manifold .. of class .., .>0, is a .. map

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An Overview of Dynamical SystemsIn previous chapters, some fundamental concepts of algebra and differential geometry were presented. This chapter is devoted to an overview of dynamical systems that play a fundamental role in building mathematical models of reality.

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Dynamics of a Material PointA positional force is said to be . with center . if its force law is . where . is the position vector relative to ..

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