scholarly journals Explicit integration of one problem of motion of the generalized Kowalevski top

2005 ◽  
Vol 32 (5) ◽  
pp. 547-552 ◽  
Author(s):  
M.P. Kharlamov ◽  
A.Y. Savushkin
Keyword(s):  
Explicit Integration ◽  
Kowalevski Top

scholarly journals Discriminantly separable polynomials and the generalized Kowalevski top

2017 ◽  
Vol 44 (2) ◽  
pp. 229-236 ◽  
Author(s):  
Vladimir Dragovic ◽  
Katarina Kukic
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Rigid Body ◽  
Constant Field ◽  
Explicit Integration ◽  
Heavy Rigid Body ◽  
Discriminantly Separable Polynomials ◽  
Integrable Dynamical Systems ◽  
Kowalevski Top

The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski?s original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top - the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.

Asymmetric FPSO Roll Response due to the Influence of Lines Arrangement

2012 ◽  
Author(s):  
Marcos Donato Ferreira ◽  
Mauro Costa de Oliveira ◽  
Rafaella Cristina Carvalho ◽  
Sergio Hamilton Sphaier
Keyword(s):  
Integration Scheme ◽  
Impulse Response Functions ◽  
Viscous Effects ◽  
Lumped Mass ◽  
Explicit Integration ◽  
Deep Waters ◽  
Campos Basin ◽  
Motion Responses ◽  
Non Linear ◽  
Ship Hydrodynamic

In the development of the mooring design of FPSOs in spread mooring system (SMS) configuration, it was observed that the utilization of asymmetric riser arrangement in deep waters might lead to an asymmetrical roll response of the FPSO. In particular, concentrating all riser connections on the portside, it could be observed that roll and heave coupling under the influence of the riser dynamics might lead to a much lower roll response associated with waves coming from portside than from the starboard direction. Simulations were carried using an in-house time domain simulator, where the ship hydrodynamic behavior was represented through the use of impulse response functions and the lines dynamic through the use of non-linear finite element method, using an explicit integration scheme and a lumped mass approach. Non-linear viscous effects could be easily associated to the ship and line velocities. Measured motion responses of an actual FPSO in operation in Campos Basin are compared with the computations.

Studies on Galloping of Iced Conductor Based on Tower-Line Coupling System – Aerodynamic Loads

2012 ◽  
Vol 182-183 ◽  
pp. 1630-1633
Author(s):  
Hao Jun Hu ◽  
Yuan Han Wang ◽  
Zi Dong Hu
Keyword(s):  
Finite Element ◽  
Wind Speed ◽  
Finite Element Model ◽  
Aerodynamic Force ◽  
Element Model ◽  
Aerodynamic Characteristics ◽  
Explicit Integration ◽  
Computing Platform ◽  
Coupling System ◽  
Line Coupling

Based on the second development at the ANSYS computing platform, finite element model of a Tower-Line Coupling system was established. The computational fluid dynamics module (CFX) was used for the numerical simulation of the aerodynamic characteristics of iced conductor. On the basis of the Kaimal spectrum, fast Fourier transform was introduced to prepare the wind speed simulation program WVFS with spatial correlation into consideration, thus generating aerodynamic coefficients of iced conductor at different wind attack angles as well as wind speed time series at tower-line nodes. According to the finite element model of continuous multi-conductors and the aerodynamic force- wind attack angle curve, the explicit integration is applied for numerical solution of galloping of iced conductor.

NOVEL COUPLING CONSTRAINT TECHNIQUE FOR EXPLICIT FINITE ELEMENT ANALYSIS

2004 ◽  
Vol 01 (02) ◽  
pp. 309-328
Author(s):  
R. J. HO ◽  
S. A. MEGUID ◽  
R. G. SAUVÉ
Keyword(s):  
Finite Element ◽  
Current Method ◽  
Explicit Integration ◽  
Rotation Tensor ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Wide Range ◽  
Large Rotations ◽  
Generalized Constraint

This paper presents a unified novel technique for enforcing nonlinear beam-to-shell, beam-to-solid, and shell-to-solid constraints in explicit finite element formulations. The limitations of classical multi-point constraint approaches are examined at length, particularly in the context of explicit solution schemes. Novel formulation of a generalized constraint method that ensures proper element coupling is then presented, and its computer implementation in explicit integration algorithms is discussed. Crucial in this regard is the accurate and efficient representation of finite rotations, accomplished using an incremental rotation tensor. The results of some illustrative test cases show the accuracy and robustness of the newly developed algorithm for a wide range of deformation, including that in which large rotations are encountered. When compared to existing works, the salient features of the current method are in evidence.

scholarly journals Surface Evolution During Semiconductor Processing

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 379-384 ◽  
Author(s):  
Ganesh Rajagopalan ◽  
Vadali Mahadev ◽  
Timothy S. Cale
Keyword(s):  
Riemann Problem ◽  
Surface Profile ◽  
Numerical Implementation ◽  
Jump Conditions ◽  
Semiconductor Processing ◽  
Explicit Integration ◽  
Surface Evolution ◽  
Left And Right ◽  
The Right ◽  
Surface Angle

We discuss our approach to using the Riemann problem to compute surface profile evolution during the simulation of deposition, etch and reflow processes. Each pair of segments which represents the surface is processed sequentially. For cases in which both segments are the same material, the Riemann problem is solved. For cases in which the two segments are different materials, two Riemann problems are solved. The material boundary is treated as the right segment for the left material and as the left segment for the right material. The critical equations for the analyses are the characteristics of the Riemann problem and the ‘jump conditions’ which represent continuity of the surface. Examples are presented to demonstrate selected situations. One limitation of the approach is that the velocity of the surface is not known as a function of the surface angle. Rather, it is known for the angles of the left and right segments. The rate as a function of angle must be assumed for the explicit integration procedure used. Numerical implementation is briefly discussed.

scholarly journals Chaplygin ball over a fixed sphere: an explicit integration

2008 ◽  
Vol 13 (6) ◽  
pp. 557-571 ◽  
Author(s):  
A. V. Borisov ◽  
Yu. N. Fedorov ◽  
I. S. Mamaev
Keyword(s):  
Explicit Integration ◽  
Chaplygin Ball

Application of a multilaminate model to simulate the undrained response of structured clay to shield tunnelling

2008 ◽  
Vol 45 (1) ◽  
pp. 14-28 ◽  
Author(s):  
H. Kien Dang ◽  
Mohamed A. Meguid
Keyword(s):  
Field Measurements ◽  
Soil Parameters ◽  
Explicit Integration ◽  
Integration Algorithm ◽  
Finite Element Program ◽  
Surface Displacements ◽  
Implicit Integration Algorithm ◽  
Element Program ◽  
Shield Tunnelling ◽  
Structured Clay

A constitutive model based on the multilaminate framework has been implemented into a finite element program to investigate the effect of soil structure on the ground response to tunnelling. The model takes into account the elastic unloading–reloading, inherent and induced anisotropy, destructuration, and bonding effects. The model is successfully calibrated and used to investigate the undrained response of structured sensitive clay in the construction of the Gatineau tunnel in Gatineau, Quebec. Numerical results were compared to the field measurements taken during tunnel construction. To improve the performance of the numerical model, an implicit integration algorithm is implemented and proven to be very effective when coupled with the multilaminate framework as compared to the conventional explicit integration methods. The effect of different soil parameters including bonding and anisotropy on the tunnelling induced displacements and lining stresses is also examined using a comprehensive parametric study. The results indicated that soil bonding and anisotropy have significant effects on the shape of the settlement trough as well as the magnitudes of surface displacements and lining stresses induced by tunnelling.

Rescaling Biology: Increasing Integration Across Biological Scales and Subdisciplines to Enhance Understanding and Prediction

2021 ◽  
Author(s):  
Colette St. Mary ◽  
Thomas H Q Powell ◽  
John S Kominoski ◽  
Emily Weinert
Keyword(s):  
Multiple Scales ◽  
Genomic Variation ◽  
Biological Processes ◽  
Explicit Integration ◽  
Fully Integrated ◽  
Community Or ◽  
Complex Processes ◽  
Spatiotemporal Scales ◽  
Patterns And Processes ◽  
Vast Range

Synopsis The organization of the living world covers a vast range of spatiotemporal scales, from molecules to the biosphere, seconds to centuries. Biologists working within specialized subdisciplines tend to focus on different ranges of scales. Therefore, developing frameworks that enable testing questions and predictions of scaling requires sufficient understanding of complex processes across biological subdisciplines and spatiotemporal scales. Frameworks that enable scaling across subdisciplines would ideally allow us to test hypotheses about the degree to which explicit integration across spatiotemporal scales is needed for predicting the outcome of biological processes. For instance, how does genomic variation within populations allow us to explain community structure? How do the dynamics of cellular metabolism translate to our understanding of whole-ecosystem metabolism? Do patterns and processes operate seamlessly across biological scales, or are there fundamental laws of biological scaling that limit our ability to make predictions from one scale to another? Similarly, can sub-organismal structures and processes be sufficiently understood in isolation of potential feedbacks from the population, community, or ecosystem levels? And can we infer the sub-organismal processes from data on the population, community, or ecosystem scale? Concerted efforts to develop more cross-disciplinary frameworks will open doors to a more fully integrated field of biology. In this paper, we discuss how we might integrate across scales, specifically by (1) identifying scales and boundaries, (2) determining analogous units and processes across scales, (3) developing frameworks to unite multiple scales, and (4) extending frameworks to new empirical systems.

A novel predictor–corrector explicit integration scheme for structural dynamics

Structures ◽  
2021 ◽  
Vol 34 ◽  
pp. 2735-2745
Author(s):  
Wei Liu ◽  
Wenhua Guo
Keyword(s):  
Structural Dynamics ◽  
Integration Scheme ◽  
Explicit Integration ◽  
Predictor Corrector
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