TY - JOUR
T1 - Duality between period and energy of certain periodic hamiltonian motions
AU - Van Groesen, E.
PY - 1986/12
Y1 - 1986/12
N2 - For a one-parameter family of periodic solutions of a second-order, autonomous, Hamiltonian system, it is shown that the minimal period T and the energy E are related in a monotone way if the even potential satisfies certain convexity and monotonicity conditions. The results are obtained using variational methods by considering the usual Lagrange functional LT and a functional JE that appears in a recent modification of the Euler–Maupertuis principle. With T and E as parameters, the values of LT and JE at certain critical points (in general, of saddle point type) define functions of T and E respectively. These functions turn out to be related by duality, from which the results follow.
AB - For a one-parameter family of periodic solutions of a second-order, autonomous, Hamiltonian system, it is shown that the minimal period T and the energy E are related in a monotone way if the even potential satisfies certain convexity and monotonicity conditions. The results are obtained using variational methods by considering the usual Lagrange functional LT and a functional JE that appears in a recent modification of the Euler–Maupertuis principle. With T and E as parameters, the values of LT and JE at certain critical points (in general, of saddle point type) define functions of T and E respectively. These functions turn out to be related by duality, from which the results follow.
UR - https://www.scopus.com/pages/publications/84963015193
U2 - 10.1112/jlms/s2-34.3.435
DO - 10.1112/jlms/s2-34.3.435
M3 - Article
AN - SCOPUS:84963015193
SN - 0024-6107
VL - s2-34
SP - 435
EP - 448
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 3
ER -