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The emergence of computers as an essential tool in scientific research has shaken the very foundations of differential modeling. Indeed, the deeply-rooted abstraction of smoothness, or <i>differentiability</i>, seems to inherently clash with a computer's ability of storing only finite sets of numbers. While there has been a series of computational… (More)

This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the coupling between their shape changes and the fluid dynamics in their environment. The equations of motion are obtained by making use of a two-stage reduction process which… (More)

Visual quality, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For example, rigid and deformable body simulation benefits greatly from conservation of linear and angular momenta. In the case of fluids, however,… (More)

— An articulated body can propel and steer itself in a perfect fluid by changing its shape only. Our strategy for motion planning for the submerged body is based on finding the optimal shape changes that produce a desired net locomotion; that is, motion planning is formulated as a nonlinear optimization problem.

We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems---an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular… (More)

On the representation, learning and transfer of spatio-temporal movement characteristics, " Int. " Humanoid robot's autonomous acquisition of proto-symbols through motion segmentation, " in Proc. IEEE Int. Conf. Transferring manipulative skills to robots: Representation and acquisition of tool manipulative skills using a process dynamics model, " J. "… (More)

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with… (More)

- Shawn C. Shadden, Jerrold Marsden, Yi Chow, Tim Colonius, Mike Cook, John Dabiri +10 others
- 2006

1 Motivation The emergence of computers as an essential tool in scientific research has shaken the very foundations of differential modeling. Indeed, the deeply-rooted abstraction of smoothness, or differentia-bility, seems to inherently clash with a computer's ability of storing only finite sets of numbers. While there has been a series of computational… (More)

- Eva Kanso, Marino Arroyo, Yiying Tong, Arash Yavari, Jerrold G Marsden, Mathieu Desbrun
- 2007

This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the… (More)