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- Mathieu Desbrun, Eva Kanso, Yiying Tong
- SIGGRAPH Courses
- 2005

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)

- Eva Kanso, Jerrold E. Marsden, Clarence W. Rowley, Juan B. Melli-Huber
- J. Nonlinear Science
- 2005

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)

- Sharif Elcott, Yiying Tong, Eva Kanso, Peter Schröder, Mathieu Desbrun
- SIGGRAPH Courses
- 2006

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.

- Liliya Kharevych, Weiwei Yang, +4 authors Mathieu Desbrun
- Symposium on Computer Animation
- 2006

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)

- Eva Kanso, Babak Ghaemi Oskouei
- 2007

This paper considers the dynamics of a rigid body interacting with point vortices in a perfect fluid. The fluid velocity is obtained using the classical complex variables theory and conformal transformations. The equations of motion of the solid-fluid system are formulated in terms of the solid variables and the position of the point vortices only. These… (More)

- Jennie Cochran, Eva Kanso, Scott David Kelly, Hailong Xiong, Miroslav Krstic
- IEEE Transactions on Robotics
- 2009

In this paper, we present a method of locomotion control for underwater vehicles that are propelled by a periodic deformation of the vehicle body, which is similar to the way a fish moves. We have developed control laws employing ldquoextremum seekingrdquo for two different ldquofishrdquo models. The first model consists of three rigid body links and relies… (More)

Balance laws are derived for the swimming of a deformable body due to prescribed shape changes and the effect of the wake vorticity. The underlying balances of momenta, though classical in nature, provide a unifying framework for the swimming of three-dimensional and planar bodies and they hold even in the presence of viscosity. The derived equations are… (More)

- EVA KANSO, PAUL K NEWTON
- 2009

The oscillations of a class of submerged mass–spring systems are examined. An inviscid fluid model is employed to show that the hydrodynamic effects couple the normal modes of these systems. This coupling of normal modes can excite the displacement mode – yielding passive locomotion of the system – even when starting with zero displacement velocity. This is… (More)

- Patrick Mullen, Alexander McKenzie, +5 authors Mathieu Desbrun
- Foundations of Computational Mathematics
- 2011

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)