Related papers: Using Lie derivatives with dual quaternions for pa…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
In this paper, we establish a local Lie theory for relative Rota-Baxter operators of weight $1$. First we recall the category of relative Rota-Baxter operators of weight $1$ on Lie algebras and construct a cohomology theory for them. We use…
The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: 1) if…
This paper describes a method for steering deformable linear objects using two robot hands in environments populated by sparsely spaced obstacles. The approach involves manipulating an elastic inextensible rod by varying the gripping…
Robot manipulation of rope-like objects is an interesting problem that has some critical applications, such as autonomous robotic suturing. Solving for and controlling rope is difficult due to the complexity of rope physics and the…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications…
We discuss the one-dimensional, general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality…
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
The simulation-to-reality (sim-to-real) transfer of large-scale hydraulic robots presents a significant challenge in robotics because of the inherent slow control response and complex fluid dynamics. The complex dynamics result from the…
Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed.…
We apply the finite-element lattice equations of motion for quantum electrodynamics given in the first paper in this series to examine anomalies in the current operators. By taking explicit lattice divergences of the vector and axial-vector…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles,…
Model-based control for robots has increasingly been dependent on optimization-based methods like Differential Dynamic Programming and iterative LQR (iLQR). These methods can form the basis of Model-Predictive Control (MPC), which is…