相关论文: Sub--Riemannian boundary value problems for Optima…

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…

The equivalence class of absolute configurations of a system under the group of similarity transformations $Sim(3)$ is called the shape of the system. The $Sim(3)$ invariant Lagrangian of the modified Newtonian theory ensures the existence…

The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…

We determine analytically the form of optimal snake locomotion when the coefficient of transverse friction is large, the typical regime for biological and robotic snakes. We find that the optimal snake motion is a retrograde traveling wave,…

Many modern learning tasks involve fitting nonlinear models to data which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training…

Snakes can traverse almost all types of environments by bending their elongate bodies in 3-D to interact with the terrain. Similarly, a snake robot is a promising platform to perform critical tasks in various environments. Understanding how…

In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots…

This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid. The objective is to minimize the hydrodynamic power…

We consider Lagrangians in Hamilton's principle defined on the tangent space $TG$ of a Lie group $G$. Invariance of such a Lagrangian under the action of $G$ leads to the symmetry-reduced Euler-Lagrange equations called the Euler-Poincar\'e…

Following Jacobi's geometrization of Lagrange's least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification…

In this paper, we investigate an optimal design problem motivated by some issues arising in population dynamics. In a nutshell, we aim at determining the optimal shape of a region occupied by resources for maximizing the survival ability of…

This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…

We construct the Lagrangian formulation of a micro-structured spinning, dilating and shearing (deformable) test body, moving in arbitrary non-Riemannian backgrounds possessing all geometrical entities of curvature, torsion and…

Stable estimation of rigid body pose and velocities from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d'Alembert principle from variational mechanics. With body-fixed optical and inertial…

In this work, we pose and solve the time-optimal navigation problem considered on a slippery mountain slope modeled by a Riemannian manifold of an arbitrary dimension, under the action of a cross gravitational wind. The impact of both…

An unsteady three-dimensional boundary element method is developed to provide fast calculations of biological and bio-inspired self-propelled locomotion. The approach uniquely combines an unsteady three-dimensional boundary element method,…

Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…

We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with recent experiments of \emph{Escherichia coli}, the polymer dynamics are…

Generalized Lagrangian mean theories are used to analyze the interactions between mean flows and fluctuations, where the decomposition is based on a Lagrangian description of the flow. A systematic geometric framework was recently developed…

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…