Abstract
Kinematics is focused on the mathematical description of motion and does not concern its dynamical causes. We shall consider the motion of particles in different coordinate systems, including Cartesian, polar (in two-dimensional 2D case), cylindrical, spherical and also in the co-moving basis which is useful in reducing 3D motion to 2D. Also we are going to deal with the kinematics of rigid bodies, which can be decomposed into a translational motion and a rotation around an instantaneous axis. Finally, we will consider the motion in an accelerated reference frame and introduce the notion of covariant derivative which is helpful, in particular, for the kinematics in rotating coordinates.
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Notes
- 1.
The particular case where \(\mathbf{v}\|\mathbf{a}\) does not require the basis that we are discussing now and can be treated in the same manner as we did in the example discussed above, at the end of the previous section.
- 2.
Without considering the case \(\hat{\mathbf{r}} = \pm \hat{\mathbf{k}}\).
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Shapiro, I.L., de Berredo-Peixoto, G. (2013). Kinematics. In: Lecture Notes on Newtonian Mechanics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7825-6_2
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DOI: https://doi.org/10.1007/978-1-4614-7825-6_2
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Publisher Name: Springer, New York, NY
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Online ISBN: 978-1-4614-7825-6
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