J. C. Simo and O. Gonzalez, Assessment of energy-momentum and symplectic schemes for sti# dynamical systems, in Winter Annual Meeting, American Society of Mechanical Engineers, New Orleans, LA, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....double spherical pendulum. We compare the double spherical pendulum algorithm to an energy momentum algorithm presented in (Wendlandt, 1995) based on the work in (Gonzalez, 1996a) In the simulations, we use energy as a monitor to catch any obvious problems, as in (Channell and Scovel, 1990) and (Simo and Gonzalez, 1993). It is still unknown if this is a reliable indicator, but based on the Ge Marsden result mentioned before, it may well be. Another indication is the analysis with energy oscillation and nearby Hamiltonian systems in (Sanz Serna, 1991) page 277 278) and (Sanz Serna and Calvo, 1994) page ....

Simo, J. and Gonzalez, O. (1993). Assessment of energy-momentum and symplectic schemes for stiff dynamical systems. In ASME Winter Annual Meeting, New Orleans. Nov. 28 - Dec. 3, 1993.

....system of index three. Since the midpoint rule and the trapezoidal rule do not converge when applied to such index three systems (17) for the direct approach [13] they usually fail when applied with large stepzsizes to highly oscillatory systems, although both methods are P stable [11, 26, 27]. We emphasize the fact that the (Rattle) Verlet al..gorithm, the midpoint rule, and the trapezoidal rule fail even if the amplitudes of the oscillations are neglectible (smooth motion) To overcome all these difficulties when solving highly oscillatory Hamiltonian and mechanical systems, we propose ....

....i = h and s 3 odd, the convergence rate is one order higher in h. As mentioned in [13] the stage order s of Gauss methods and Lobatto IIIA methods has to be sufficiently high to ensure convergence. The midpoint rule and the trapezoidal rule do not converge. This has been numerically observed in [11, 26, 27]. For the solution of oscillatory systems, any numerical scheme obviously introduces phase errors up to its order of accuracy. A phase error analysis of Runge Kutta methods can be found in [29] where forcing oscillating forces have also been considered. It has even been proved in [28] that ....

J. C. Simo and O. Gonzalez, Assessment of energy-momentum and symplectic schemes for stiff dynamical systems, Tech. Report 93-WA/PVP-4, Div. of Appl. Mech., Dept. of Mech. Eng., Stanford Univ., U.S.A., 1993.

....a method for constructing energy momentum integrators for mechanical systems that involve holonomic constraints. The following algorithm was constructed based on Oscar s general construction. Several useful references for energy momentum integrators are [Gonzales and Simo, 1994] Tarnow, 1993] [Simo and Gonzalez, 1993], and [Simo and Tarnow, 1992] Oscar Gonzalez s general construction for energy momentum integrators is briefly summarized in this section. The construction introduces a discrete differential which is analogous to the continuous differential. The defining properties of the discrete differential, D ....

Simo, J. and Gonzalez, O. (November 28 - December 3, 1993). Assessment of energy-momentum and symplectic schemes for stiff dynamical systems. In ASME Winter Annual Meeting, New Orleans.

....the ideal model first, and then one can use a time splitting (product formula) method to interleave it with ones favorite dissipative method one wishes to use. Energy as a Monitor. In the simulations, we use energy as a monitor to catch any obvious problems, as in (Channell and Scovel, 1990) and (Simo and Gonzalez, 1993). It is still unknown if this is a reliable indicator, but based on the Ge Marsden result mentioned before, it may well be. Another indication is the J.M. Wendlandt and J.E. Marsden analysis with energy oscillation and nearby Hamiltonian systems in (Sanz Serna, 1991) page 277 278) and ....

Simo, J. and Gonzalez, O. (1993). Assessment of energy-momentum and symplectic schemes for stiff dynamical systems. In ASME Winter Annual Meeting, New Orleans. Nov. 28 - Dec. 3, 1993.

No context found.

J. C. Simo and O. Gonzalez, Assessment of energy-momentum and symplectic schemes for sti# dynamical systems, in Winter Annual Meeting, American Society of Mechanical Engineers, New Orleans, LA, 1993.

No context found.

J. C. Simo and O. Gonzalez, Assessment of energy-momentum and symplectic schemes for stiff dynamical systems, Tech. Report 93-WA/PVP-4, Div. of Appl. Mech., Dept. of Mech. Eng., Stanford Univ., U.S.A., 1993.

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