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Results tagged with classical-mechanics
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user 5371
Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.
2
votes
How can I conclude that I live in a solar system?
An interesting (and very old) argument in favour of heliocentrism is based on estimates of the relative sizes of the Earth and Sun.
Actually, Aristarchus of Samos estimated that the Sun is six to …
- 22.3k
5
votes
Accepted
Rolling a convex body: Geodesics vs. rolling curves
The rolling motion of a convex symmetric body on a horizontal plane is a classical problem. In the symmetric case, Chaplygin was the first who showed that the full equations of motion can be reduced t …
- 22.3k
29
votes
Accepted
On the non-rigorous calculations of the trajectories in the moon landings
The existence of the Arenstorf Orbits was discovered in 1963 on the basis of numerical computations. The Arenstorf orbits appear as periodic solutions to the equations for the plane restricted three b …
- 22.3k
2
votes
Newton equations, second order equation and (im)possible motions
Newton's second law implies basically that the evolution of a mechanical system is completely determined as soon as the particles' initial positions $x(0)$ and velocities $\dot x(0)$ are specified. S …
- 22.3k
52
votes
Accepted
Geometric interpretation of the half-derivative?
A possible mechanical interpretation of the half-derivative can be given in terms of Abel's solution to a classical problem from the calculus of variations (the tautochrone problem).
Let there be a …
- 22.3k
29
votes
Accepted
Parabolic envelope of fireworks
E. Torricelli, who was the last Galileo's secretary, suggested a purely geometrical method to find the envelope in his De motu Proiectorum. He also coined the term `parabola of safety'. Apparently i …
- 22.3k
17
votes
Accepted
Surface equivalent of catenary curve
A model equation for an inextensible, flexible, heavy surface in a gravitational field was deduced by Poisson Lagrange and later the problem was also studied by Poisson (see the references in the link …
- 22.3k