Abstract
The following is a compilation of essential mathematical tools needed in theoretical mechanics. A transparent connection between the tool and its application is favored over mathematical rigor.
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Notes
- 1.
Euler, Leonhard, Swiss mathematician and physicist, *Basel 15.4.1707, †St. Petersburg 18.9.1783; he made numerous important contributions to mathematics, physics, and astronomy.
- 2.
Notice that the expansion does satisfy the derivation rule (1.59).
- 3.
Carl Friedrich Gauss, 1777–1855, made outstanding contributions to mathematics, physics as well as astronomy.
- 4.
Strictly speaking ‘equal but opposite’ would mean that nothing happens. The situation is one of static equilibrium. We assume however that Sisyphus pushed just hard enough to overcome the force of gravity by a ‘negligible’ amount without causing ‘noticeable acceleration’.
Reference
M.R. Spiegel, Advanced Mathematics - Schaum’s Outline Series in Mathematics (McGraw-Hill, New York, 1971)
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Hentschke, R. (2017). Mathematical Tools. In: Classical Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-48710-6_1
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DOI: https://doi.org/10.1007/978-3-319-48710-6_1
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