On the motion of a heavy point along a rough helical surface with a vertical axis
Authors:
Abstract
Let FT and Fn be the absolute values of the tangential and normal to the surface components of the weight force acting on a point. A point placed on the surface without initial velocity remains in equilibrium in the presence of friction if FT≤kFn, and begins to move if FT>kFn, where k is the coefficient of friction. The differential equations of motion of a point M of weight g on a rough surface (r, φ, z)=0 in cylindrical coordinates r, φ, z (the z-axis is directed vertically downward) are given in the article.
Funding:
None
References
- Applied Mathematics and Mechanics, Vol. 1, Issue 1, Page 56b, 1933. (In Russian)
- Archives of Mathematics and Physics, 3rd edition, Vol. 5b, Page 28, 1903. (In Russian)
- Goursat, Course of Mathematical Analysis, Vol. 1, Sections 233–236, 1933. (In Russian)
- Goursat, Course of Mathematical Analysis, Vol. 1, Section 250, 1933. (In Russian)
- Appel, Handbook of Theoretical Mechanics, Vol. 1, Section 259, 1911. (In Russian)
- Zapiski Gornogo instituta, Vol. 10, Issue 1, Pages 1 and 31, 1935. (In Russian)
- Zapiski Gornogo instituta, Vol. 12, Issue 3, p. 23 and 31, 1939. (in Russian)
- Picard, Traité d'analyse, vol. 3, p. 22, Paris, 1896.
- L.B. Levenson, Spiral Separator, p. 53, Leningrad, 1925. (in Russian)
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