Search results for "Equations of motion"
showing 10 items of 143 documents
Communication: multireference equation of motion coupled cluster: a transform and diagonalize approach to electronic structure.
2014
The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective…
Introducing Memory in Coarse-Grained Molecular Simulations
2021
[Image: see text] Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori–Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In…
Dynamic Modeling of Planar Multi-Link Flexible Manipulators
2021
A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.
Adapted Approach for Omnidirectional Egomotion Estimation
2011
Egomotion estimation is based principally on the estimation of the optical flow in the image. Recent research has shown that the use of omnidirectional systems with large fields of view allow overcoming the limitation presented in planar-projection imagery in order to address the problem of motion analysis. For omnidirectional images, the 2D motion is often estimated using methods developed for perspective images. This paper adapts motion field calculated using adapted method which takes into account the distortions existing in the omnidirectional image. This 2D motion field is then used as input to the egomotion estimation process using spherical representation of the motion equation. Expe…
A NEW SYMMETRIC AND POSITIVE DEFINITE BOUNDARY ELEMENT FORMULATION FOR LATERAL VIBRATIONS OF PLATES
1997
Abstract A new symmetric and positive definite boundary element method in the time domain is presented for the dynamic analysis of thin elastic plates. The governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed. The functional is expressed in terms of the domain and boundary basic variables in plate bending, assumed to be independent of each other. In the discretized model the boundary variables are expressed by nodal values, whereas the internal displacement field is modelled by a superposition of static fundamental solutions. The equations of motion are deduced from the functional stationarity conditions and they cons…
Dynamic stability of plane elastic frames
1982
Abstract The stability of plane elastic frames subjected to a vertical foundation motion of the stationary, ergodic type is investigated. The equations of motion are obtained in modal co-ordinates, with account taken of many modes of vibration. The problem is subsequently reduced to the study of only the first mode of vibration. By considering a particular case, the stability domains are sketched as functions of the variation of the rigidities of the beam-column connecting joints and as functions of the number of stories.
Functional Derivative Approach
2001
Let us now leave the path integral formalism temporarily and reformulate operatorial quantum mechanics in a way which will make it easy later on to establish the formal connection between operator and path integral formalism. Our objective is to introduce the generating functional into quantum mechanics. Naturally we want to generate transition amplitudes. The problem confronting us is how to transcribe operator quantum mechanics as expressed in Heisenberg’s equation of motion into a theory formulated solely in terms of c-numbers. This can be achieved either by Schwinger’s action principle or with the aid of a generation functional defined as follows:
The planar two-body problem for spheroids and disks
2021
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral, and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not invol…
A gradient elasticity theory for second-grade materials and higher order inertia
2012
Abstract Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the …