Weinstein

It is sometimes very usefiil to look at a trajectory such as the synnnetric or antisynnnetric stretch of figure Al.2.5 and figure A1.2.6 not in the physical spatial coordinates (r. . r y), but in the phase space of Hamiltonian mechanics [16, 29], which in addition to the coordinates (r. . r ) also has as additional coordinates the set of conjugate momenta. . pj. ). In phase space, a one-diniensional trajectory such as the aiitisymmetric stretch again appears as a one-diniensional curve, but now the curve closes on itself Such a trajectory is referred to in nonlinear dynamics as a periodic orbit [29]. One says that the aihiamionic nonnal modes of Moser and Weinstein are stable periodic orbits. 

Weinstein A 1973 Normal modes for nonlinear Hamiltonian systems Inv. Math. 20 47... 

Moser J 1976 Periodic orbits near an equilibrium and a theorem by Alan Weinstein Comm. Pure Appl. Math. 29 727... 

A. O. PaUingston and M. Weinstein, Method of Calculation of Interior Ballistic Properties of Propellantsfrom ClosedBomb Data, report 2005, PTA, Dover, N.J., 1959. 

R. E. Weinstein and R. B. Boulay, in Proc. ofi26th Sjmposium on Engineering Aspects ofiMHD, Nashville, Term., June 1988, pp. 8.5.1—8.5.9. 

J. Weinstein, D. J. Cooper, and P. J. L. Daniels, Mbstracts, 12th Intersci. Conf. Mntimicrob. Mgents Chemother. 9 (1972). 

A. W. Weinstein and co-workers. Products liability and the Keasonablj Safe Product, ]ohxi Wiley Sons, Inc., New York, 1978. 

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