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Eizi Hirota - One of the best experts on this subject based on the ideXlab platform.
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internal motions in a complex consisting of a rare gas atom and a c2v molecule theoretical formulations and their applications to fourier transform microwave spectra of ne dimethyl ether and ar dimethyl ether
Journal of Chemical Physics, 2006Co-Authors: Yasumasa Morita, Nobukimi Ohashi, Yoshiyuki Kawashima, Eizi HirotaAbstract:The internal motion of the rare gas atom, i.e., the relative motion of the two constituents, in a complex shown in the title was discussed by paying special attention to its effect on the rotational motion of the complex in order to extract as much precise information on this motion as possible from the observed rotational spectra. We have set up two theoretical formulations. One is based on a Coordinate axis System attached to the C2v molecule, but its origin is floating with the motion of the rare gas atom, while keeping the orientation parallel to the original C2v molecule-Fixed Coordinate System. The second approach starts with counting the number of equivalent potential minima, which are well separated from the others by high potential barriers, and then collects all permutation-inversion operations, which transform the System from one minimum to another, to set up a group appropriate for the complex. By using the symmetry properties thus derived, a phenomenological Hamiltonian is set up to fit the o...
H Kleinert - One of the best experts on this subject based on the ideXlab platform.
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motion of a rigid body in body Fixed Coordinate System for autoparrallel trajectories in spaces with torsion
arXiv: High Energy Physics - Theory, 1995Co-Authors: P Fiziev, H KleinertAbstract:We use a recently developed action principle in spaces with curvature and torsion to derive the Euler equations of motion for a rigid body within the body-Fixed Coordinate System. This serves as an example that the particle trajectories in a space with curvature and torsion follow the straightest paths (autoparallels), not the shortest paths (geodesics), as commonly believed.
Koichi Hashiguchi - One of the best experts on this subject based on the ideXlab platform.
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objectivity and corotational rate tensor
2009Co-Authors: Koichi HashiguchiAbstract:The mechanical properties of a material are independent of the reference frame of the observer. Therefore, a constitutive equation describing the properties must be invariant under the change of Coordinate System mutually rotating with respect to each other. The physical meaning of this type of the objectivity of constitutive equations and the general form of corotational rate of a tensor that has to be used in stead of the usual material-time derivative (under the Fixed Coordinate System) in order to fulfill the invariance are described in this chapter.
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general corotational rate tensor and replacement to corotational derivative of yield function
ICCES: International Conference on Computational & Experimental Engineering and Sciences, 2007Co-Authors: Koichi HashiguchiAbstract:Introduction Mechanical property of materials are observed to be identical independent of states of observers. Then, it should be described by a unique equation independent of mutual configuration and/or rotation between material and observers. This fact is called the principle of material-frame indifference [1]. On account of this principle, all of physical quantities used in constitutive equations have to be described by the tensor quantities obeying the common translation rule, called the objective transformation, between Coordinate Systems. In particular, constitutive equation of inelastic deformation has to be formulated as the relation between rate variables through the stress and internal variables. Whilst all state quantities obey the objective transformation, pertinent tensors obeying the objective transformation independent of material rotation have to be adopted for their rate variables. In addition, they have to be physical quantities capable of describing rates of mechanical state appropriately evaluating a rotation of material. They can be given by the corotational rate tensors which have components obtained by the objective inverse-transformation from the components observed by the Coordinate System rotating with material to the Fixed Coordinate System describing the constitutive relation. Besides, in the formulation of plastic constitutive equation the consistency condition is obtained first by material-time differentiation of yield condition. In order to use it as a constitutive relation one has to translate the stress rate and rates of internal variables to their corotational rate. In this note a general corotational rate for tensors in arbitrary order having the objectivity is shown first. Further, it is verified that the material-derivative of yield condition involving arbitrary tensors can be replaced to the corotational derivative, i.e. the consistency condition which can be used as a constitutive relation.
Odd M. Faltinsen - One of the best experts on this subject based on the ideXlab platform.
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Linear seakeeping and added resistance analysis by means of body-Fixed Coordinate System
Journal of Marine Science and Technology, 2012Co-Authors: Yan-lin Shao, Odd M. FaltinsenAbstract:This paper presents an alternative formulation of the boundary value problem for linear seakeeping and added resistance analysis based on a body-Fixed Coordinate System. The formulation does not involve higher-order derivatives of the steady velocity potential on the right-hand side of the body-boundary condition, i.e., the so-called m _ j -terms in the traditional formulation when an inertial Coordinate System is applied. Numerical studies are made for a modified Wigley I hull, a Series 60 ship with block coefficient 0.7, and the S175 container ship for moderate forward speeds where it is thought appropriate to use the double-body flow as basis flow. The presented results for the forced heave and pitch oscillations, motion responses, and added resistance in head-sea waves show good agreement with experiments and some other numerical studies. A Neumann–Kelvin formulation is shown to give less satisfactory results, in particular for coupled heave and pitch added mass and damping coefficients.
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use of body Fixed Coordinate System in analysis of weakly nonlinear wave body problems
Applied Ocean Research, 2010Co-Authors: Yan-lin Shao, Odd M. FaltinsenAbstract:Abstract When a weakly nonlinear wave–body problem is considered in an inertial Coordinate System, high-order derivatives appear in the higher-order body boundary conditions and make it difficult to get convergent and accurate results, especially for bodies with sharp corners or high surface curvatures. In this paper, a new method taking the advantage of the accelerated body-Fixed Coordinate System is proposed to avoid derivatives of the velocity potential on the right-hand side of the body boundary conditions. A domain decomposition method is applied with the use of the body-Fixed Coordinate System in the inner domain and the Earth-Fixed Coordinate System in the outer domain. The second-order radiation and diffraction of bodies with and without sharp corner are studied in the time domain and verified. A numerical beach is applied. Unlike the other methods which transfer the high-order derivatives to lower-order ones by using Stokes-like theorems, it is straightforward to generalize the present method to higher than second-order radiation problems and to the nonlinear wave–body analysis when the forward speed or current is included.
Stefan Kraneburg - One of the best experts on this subject based on the ideXlab platform.
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analysis of body surfaces in a body Fixed Coordinate System
2007Co-Authors: B Drerup, Stefan KraneburgAbstract:Visualisation of shape and shape change e.g. by contour lines depends on the selection of the Coordinate System of the contour levels. This is elucidated by using the plaster cast of a scoliotic back being rotated in front of a 3-D measurement and analysis System. Axial rotation through an axis parallel to the contour planes results in a dramatic change of the contour patterns on the back. This is in contrast to the expectation of the ingenuous viewer interpreting the contour line pattern like a fingerprint. To meet this attitude shape analysis must be referenced to a body Fixed Coordinate System, which may be defined by anatomical landmarks. It is shown, that vertebra prominens and the lumbar dimples provide anatomical landmarks capable for this purpose.