10 citations · 35 across the 9 of their papers we have counts for
9 papers
New second-order optimality conditions in sub-Riemannian Geometry
Michał Jóźwikowski
We study the geometry of the second-order expansion of the extended end-point map for the sub-Riemannian geodesic problem. Translating the geometric reality into equations we deriv…
Higher derivatives of the end-point map of a linear control system via adapted coordinates
Michał Jóźwikowski, Bartłomiej Sikorski
We study the end-point map of a control-linear system in a neighborhood of an arbitrarily chosen trajectory. In particular, we want to calculate the -th order derivative of this…
Prolongations vs. Tulczyjew triples in Geometric Mechanics
Michał Jóźwikowski
In the scientific literature there are basically two schools of formulating Lagrangian (or Hamiltonian) mechanics in the (Lie) algebroid setting: in terms of prolongations and in t…
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms
Michał Jóźwikowski, Mikołaj Rotkiewicz
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as ve…
Duality for graded manifolds
Janusz Grabowski, Michał Jóźwikowski, Mikołaj Rotkiewicz
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we…
Why are normal sub-Riemannian extremals locally minimizing?
Michał Jóźwikowski, Witold Respondek
It is well-known that normal extremals in sub-Riemannian geometry are curves which locally minimize the energy functional. Most proofs of this fact do not make, however, an explici…
A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems
Michał Jóźwikowski, Witold Respondek
We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations a…
Prototypes of higher algebroids with applications to variational calculus
Michał Jóźwikowski, Mikołaj Rotkiewicz
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also const…
Bundle-theoretic methods for higher-order variational calculus
Michał Jóźwikowski, Mikołaj Rotkiewicz
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order varia…