Note on classical Hamiltonian theory. (English. Russian original) Zbl 0149.42006
PMM, J. Appl. Math. Mech. 24, 40-42 (1960); translation from Prikl. Mat. Mekh. 24, 33-34 (1960).
Verf. untersucht die Frage nach einer Schranke, innerhalb der ein mechanisches System unempfindlich gegenüber Zusatzkräften ist, die von höherer als der ersten Ordnung klein sind. Er kommt anhand früherer Arbeiten von Lyapunov und sich selbst zu dem Ergebnis, daß es sich bei dieser Schranke um Kräfte handelt, die von einer positiv definiten quadratischen Dissipationsfunktion erzeugt werden.
Reviewer: Helmut Rüßmann
MSC:
| 70H05 | Hamilton’s equations |
References:
| [1] | Liapunov A.M., Obshchaia zadacha ob ustoichivosti dvizheniia (The general problem of stability of motion; Liapunov A.M., Obshchaia zadacha ob ustoichivosti dvizheniia (The general problem of stability of motion |
| [2] | Chetaev, N. G., Ob ustoichivykh traektoriiakh dinamiki, Uchenye zapiski Kazan. Universiteta, Vol. 91, No. 1 (1931), Book 4 |
| [3] | Chetaev, N. G., Ob odnoi zadache Koshi, PMM, Vol. 9, No. 2 (1945) |
| [4] | Liapunov A.M., K voprosu ob ustoichivosti dvizheniia (On the problem of stability of motion; Liapunov A.M., K voprosu ob ustoichivosti dvizheniia (On the problem of stability of motion |
| [5] | Chetaev, N. G., Ustoichivost’ dvizheniia, ((1946), Gos. Izdat. Tekhn. Teor. Lit.: Gos. Izdat. Tekhn. Teor. Lit. Moscow-Leningrad), 102 |
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