Titlebook: Classical Mechanics with Mathematica?; Antonio Romano,Addolorata Marasco Textbook 2018Latest edition Springer International Publishing AG,

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Exterior Derivative and Integratione exterior derivative extends to .-forms the elementary definitions of gradient of a function, curl, and divergence of a vector field as well as the meaning of exact and closed 1-forms. The integration of .-forms allows to extend the definitions of surface and volume integrals as well as the Gauss and Stokes theorems.

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Kinematics of?Rigid Bodiesnslational, rotational, spherical, and planar motions are studied. Finally, the transformation formulae of velocity and acceleration from a rigid frame of reference to another one are determined. Exercises conclude the chapter.

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Principles of Dynamicsen, the Newton laws are recalled together with some important consequences (momentum balance, angular momentum balance, kinetic energy, K?nig’s theorem). Dynamics in noninertial frames both in the absence and in the presence of constraints is presented together with some exercises of point dynamics.

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Dynamics of?a?Rigid Bodyoment of forces vanishes are studied: Poinsot’s motions, uniform rotations, and inertial motions of a gyroscope. The different properties of motion of a heavy gyroscope and the gyroscopic effect are analyzed. Finally, the motions of Foucault’s gyroscope, gyroscopic compass, and free heavy solid are taken into account.

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Classical Mechanics with Mathematica?978-3-319-77595-1Series ISSN 2164-3679 Series E-ISSN 2164-3725

LVAD360

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Anabel Ternès,Christopher Runge In other words, we show the existence of an isomorphism between . and ., of isomorphisms between ., ., and ., and so on. These isomorphisms lead to the definitions of Euclidean vectors, tensors, and to the covariant, contravariant, and mixed components of a tensor.

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Anabel Ternès,Christopher Rungenslational, rotational, spherical, and planar motions are studied. Finally, the transformation formulae of velocity and acceleration from a rigid frame of reference to another one are determined. Exercises conclude the chapter.