相关论文: Solving Linearized Equations of the $N$-body Probl…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing…
We review elliptic solutions to integrable nonlinear partial differential and difference equations (KP, mKP, BKP, Toda) and derive equations of motion for poles of the solutions. The pole dynamics is given by an integrable many-body system…
We introduce a numerical method for the numerical solution of the so-called Lur'e matrix equations that arise in balancing-related model reduction and linear-quadratic infinite time horizon optimal control. Based on the fact that the set of…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multi-body systems. Although the motion of multi-body systems is considered to be a well-studied problem and…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be…
In inertial motion capture, a multitude of body segments are equipped with inertial sensors, consisting of 3D accelerometers and 3D gyroscopes. Using an optimization-based approach to solve the motion capture problem allows for natural…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques,…
We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei…
We consider methods for constructing explicit solutions of the non-stationary Lam\'e equation, which is a generalization of the classical Lam\'e equation, that has appeared in works on integrable models, conformal field theory, high energy…
We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…