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Soft robots are interesting examples of hyper-redundancy in robotics, however, the nonlinear continuous dynamics of these robots and the use of hyper-elastic and visco-elastic materials makes modeling of these robots more complicated. This…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
This paper introduces an analytical framework for the derivation of hybrid equations of motion of a flexible quadrotor. This approach helps obtain rigid and elastic equations of motion simultaneously, in a decoupled form, which facilitates…
Higher Time Derivative Theories are generated by considering space-time rotated KdV and mKdV systems. These systems are then studied to see if/how instabilities, usually associated with higher time derivative theories, manifest on the…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
This study presents a comprehensive evaluation of dynamic aerodynamic derivatives during aircraft transition phases using advanced CFD simulations and forced oscillation testing. Two case studies are examined: a three dimensional fighter…
The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…
Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…
By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…
In this paper some new physical notations are given for the Green's functions and equations of motion (EOM) in many body physics with the concept of quasiparticles. It shows how the many body correlations existing in many body systems can…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…
Deformable object manipulation (DOM) is an emerging research problem in robotics. The ability to manipulate deformable objects endows robots with higher autonomy and promises new applications in the industrial, services, and healthcare…
This paper proposes a novel modelling approach for a heavy-duty manipulator with parallel$-$serial structures connected in series. Each considered parallel$-$serial structure contains a revolute segment with rigid links connected by a…
While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…