 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12949 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8096
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| In English (Mech. Solids): | | 4853 |
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| A.G. Petrov, "On Forced Oscillations of a Double Mathematical Pendulum," Mech. Solids. 59 (4), 1898-1908 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
4 |
Pages |
1898-1908 |
| DOI |
10.1134/S0025654424603288 |
| Title |
On Forced Oscillations of a Double Mathematical Pendulum |
| Author(s) |
A.G. Petrov (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, petrovipmech@gmail.com) |
| Abstract |
For conservative mechanical systems, the method of normal coordinates is known, which
uses the theorem on the reduction of two quadratic forms to the sum of squares. In this case, the system
of differential equations is split into a system of independent oscillators. A linear dissipative mechanical system with a finite number of freedom degrees is defined by three quadratic forms: the kinetic
energy of the system and potential energy of the system, and the dissipative Rayleigh function.
We study the linear problem of forced oscillations of a double pendulum when the friction coefficients
are proportional to the masses. Then all three quadratic forms are reduced to the sum of squares by a
single transformation. In normal coordinates the system splits into two independent systems of second order. An analytical solution is constructed in the most general form for arbitrary rod lengths and point
masses. A complete analysis of the oscillations in the non-resonant case and in the case of resonances is given. Formulas for the error of the analytical formulas if the proportionality of the friction coefficients and masses is violated are also obtained. |
| Keywords |
Lagrange method, double pendulum, quadratic forms, normal coordinates, dissipative systems |
| Received |
05 March 2024 | Revised |
24 March 2024 | Accepted |
25 March 2024 |
| Link to Fulltext |
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