摘要 :
Although it is widely recognized by structural researchers that sequentialrotations about axes fixed in space are not commutative, there prevails confusion in the literature about different definitions of rotations and different r...
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Although it is widely recognized by structural researchers that sequentialrotations about axes fixed in space are not commutative, there prevails confusion in the literature about different definitions of rotations and different rotational parameters employed in handling compound spatial rotations. Different definitions of rotations or different parameters have been referred to by the same name and vice versa, and computation algorithms that are valid for certain types of rotation have been applied indiscriminately. Some researchers misunderstand the relationships between rotations and moments in space, and others fail to grasp the implications of certain types of rotation in the second-order analysis of space frames. The present work describes eight definitions for spatial rotations and points out their implications in the second-order analysis of space frames subjected to conservative loads. A redefinition of semi-tangential rotations as vectorial rotations is also proposed.
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It is shown that a possibly redundant robot with rigid links driven at the nodes can be stabilized for any feasible, given path of the nodes. This result is generalized to robots with stiff yet flexible links. The Lagrangean equat...
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It is shown that a possibly redundant robot with rigid links driven at the nodes can be stabilized for any feasible, given path of the nodes. This result is generalized to robots with stiff yet flexible links. The Lagrangean equations of motion are used to describe the robot. The controls are the polygenic generalized forces corresponding to the Lagrangean coordinates. The stabilizing controls are exhibited.
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We revisit the Lagrange and Delaunay systems of equations of celestial mechanics, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the...
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We revisit the Lagrange and Delaunay systems of equations of celestial mechanics, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom of choice (=freedom of gauge fixing) reveals a symmetry hiding behind Lagrange’s and Delaunay’s systems, which is, mathematically, analogous to the gauge invariance in electrodynamics. Just like a convenient choice of gauge simplifies calculations in electrodynamics, so the freedom of choice of the submanifold may, potentially, be used to create simpler schemes of orbit integration. On the other hand, the presence of this feature may be a previously unrecognised source of numerical instability.
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The problem of Lagrangian chaos (of the chaotic motion of fluid particles) isreviewed using methods and tools borrowed from the theory of dynamical systems. The main subject is the behavior of fluid particles which move according ...
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The problem of Lagrangian chaos (of the chaotic motion of fluid particles) isreviewed using methods and tools borrowed from the theory of dynamical systems. The main subject is the behavior of fluid particles which move according to regular velocity fields, that is, in the absence of Eulerian chaos or turbulence. In this framework, particular attention is given to the relation with mixing, transport, and diffusion phenomena in fluids. A possible general mechanism for the onset of Lagrangian chaos in two dimensional fluids is discussed. Evidence that the presence of a chaotic velocity field (Eulerian chaos) is not relevant for many properties of the particle motion is provided. Similar methods are applied to the analysis of the properties of the small scale statistics of passive scalar and magnetic fields. The long time diffusion features of contaminant particles, which show the importance of the combined effect of the molecular diffusion and the geometrical structures of the velocity field, are also studied.
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A fully adaptive, moving grid method was developed for solving initial-boundary value problems for systems of one-space dimensional partial differential equations (PDE) whose solutions exhibit rapid variations in space and time. T...
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A fully adaptive, moving grid method was developed for solving initial-boundary value problems for systems of one-space dimensional partial differential equations (PDE) whose solutions exhibit rapid variations in space and time. The method, based on finite differences, is of the Lagrangian type and was derived through a coordinate transformation which leads to equidistribution in space of the second derivative. The technique is intermediate between static regridding methods, where nodes remain fixed for intervals of time, and continuously moving grid methods, where the node movement and the PDE integration are fully coupled. The computation of the moving grids and the solution on these grids are carried out separately, while the nodes are moved at each time-step. Two error monitors were implemented, one to govern the time step selection and the other to adapt the number of moving nodes. The method allows the use of different moving grids for different components in the PDE system. Numerical experiments are presented for a set of five sample problems from the literature, including two problems from combustion.
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Basic mechanical concepts from the Central Field to Lagrangian and Delanay Equations are presented. Orbital determination, reference systems and their transformation are also presented.
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A three dimensional Lagrangian pollutant dispersal model for passive contaminants was modified to allow simulation of dispersal of heavy gases, and moist and buoyant plumes. Outputs from a two dimensional Navier-Stokes atmospheric...
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A three dimensional Lagrangian pollutant dispersal model for passive contaminants was modified to allow simulation of dispersal of heavy gases, and moist and buoyant plumes. Outputs from a two dimensional Navier-Stokes atmospheric boundary layer solver are used. Model runs were made to simulate experimental tests of gas dispersion in atmospheric surface layers. Predicted concentration fields are in accord with measurement. Model simulation of water vapor plume dispersal in the planetary boundary layer were made using field data from cooling towers. Predicted plume rise and visible plume outline are in good agreement with observations for various meteorological and source conditions.
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