Runge-Kutta collocation methods for rigid body Lie-Poisson equations

The rigid body Lie-Poisson structure in three dimensions is considered. We show that the symplectic collocation type Runge-Kutta methods preserve the one-form of the underlying system. The linear error growth, energy and momentum conservation properties of the numerical solutions are discussed for Euler top equation.


Poisson integrators for Volterra lattice equations
Ergenc, T; Karasözen, Bülent (2006-06-01)
The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the symplectic Euler and second order Lobatto IIIA-B method. Numerical results confirm preservation of the corresponding Hamiltonians, Casimirs, quadratic and cubic integrals in the long-term with different orders of accuracy. (c) 2005 IMACS. Published by Elsevier B.V. All rights re...
Reduced order modeling of helicopter substructures for dynamic analysis
Hayırlı, Uğur; Kayran, Altan; Department of Aerospace Engineering (2018)
Dynamic analysis of a structure is generally conducted by the finite element method in aerospace structures. The models usually contain large number of elements to be able to obtain more accurate results. Although the most computers are capable of solving the large and complex problems, the analysis problems such as dynamic optimization, aeroelastic, frequency and time response may take long time due to involving iterative and multi-step processes. In this study, various model reduction methods are describe...
Dynamic modeling of structural joints
Tol, Şerife; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2012)
Complex systems composed of many substructures include various structural joints connecting the substructures together. These mechanical connections play a significant role in predicting the dynamic characteristics of the assembled systems accurately. Therefore, equivalent dynamic models of joints that consist of stiffness and damping elements should be developed and the joint parameters should be determined for an accurate vibration analysis. Since it is difficult to estimate joint parameters accurately by...
Generalized coutte flow of herschel-bulkley fluid through eccentric annulus-an approximate solution
Seyidoğlu, Tijen; Tosun, İsmail; Department of Chemical Engineering (2006)
Generalized Couette flow of a Herschel-Bulkley fluid in an eccentric annulus is analyzed by approximating the flow geometry as a slit of variable height. Besides an imposed pressure gradient, one of the plates is considered non-stationary to take into account the axial and/or angular motion of the inner pipe in an eccentric annulus system. Depending on the magnitude and the direction of the applied pressure gradient with respect to the plate velocity, three separate flow cases are studied in which the veloc...
Procedure for determining seismic vulnerability of building structures
Gulkan, P; Sozen, MA (1999-05-01)
A rationalization for ranking reinforced concrete frame buildings with masonry infill walls with regard to seismic vulnerability is presented The method essentially requires only the dimensions of the structure as input, and is expressed in terms of where its attributes are located in a two-dimensional plot of masonry wall and column percentages. It is shown that increasing drift at the ground story (which is a reasonable expression of increasing vulnerability) is attained by decreasing either attribute It ...
Citation Formats
T. Ergenc and B. Karasözen, “Runge-Kutta collocation methods for rigid body Lie-Poisson equations,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 63–71, 1996, Accessed: 00, 2020. [Online]. Available: