Browsing by Author "Leine, Remco I. (Prof. Dr. ir. habil.)"

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Open Access
Dynamics of finite-dimensional mechanical systems
(2019) Winandy, Tom; Leine, Remco I. (Prof. Dr. ir. habil.)
This monograph deals with the description of mechanical systems having finitely many degrees of freedom using the language of global differential geometry. The mechanical systems may be explicitly time-dependent and involve nonpotential forces. The focus is on the mathematically rigorous formulation of the physical theory dealing with the aforementioned mechanical systems with the objective to introduce the involved physical quantities as well-defined mathematical objects. The geometric presentation of the physical theory is erected upon a generalized space-time known as Galilean manifold. The state space of a mechanical system is defined as an affine subbundle of the tangent bundle of its associated Galilean manifold. The system's motion is considered to be an integral curve of a second-order vector field on the state space. With the coordinate-free characterization of the motion in terms of second-order vector fields, differential forms appear on stage. A one-to-one correspondence between second-order vector fields and action forms is established. Action forms are differential two-forms with additional properties. The definition of action forms and the derivation of this bijective relation relies on the geometry of double tangent bundles, in which vector bundle homomorphisms and their differential concomitants play an important role. A coordinate-free definition of forces is given and different geometric interpretations are discussed. With the definition of kinetic energy and of potential forces, the equations of motion are postulated in a coordinate-free way using the action form of the mechanical system. Lagrange's, Hamel's, and Hamilton's equations become local representations of this postulate in terms of a respective chart of the state space. Moreover, the connection between action forms and the concept of virtual work is established. This allows to obtain Lagrange's and Hamel's central equation. This variational perspective is pursued by showing that motions characterized by an exact action form satisfy Hamilton's principle. For this purpose, a coordinate-free definition of the action integral is given. Finally, constraints are defined as distributions compatible with the time structure of the Galilean manifold on which they are defined. Consequently, the distinction between holonomic and nonholonomic constraints is made using the Frobenius theorem.
Open Access
Mechanical systems with frictional contact : geometric theory and time discretization methods
(2021) Capobianco, Giuseppe; Leine, Remco I. (Prof. Dr. ir. habil.)
This dissertation deals with the mathematical description and the simulation of mechanical systems with frictional contact. First, a geometric theory for the description of smooth mechanical systems is developed, which is then extended to allow for nonsmooth motions, i.e., motions with discontinuous velocities. The developed nonsmooth theory of mechanics is used to describe mechanical systems with frictional contact. Finally, two numerical schemes for the simulation of such systems are derived by using a time finite element method and the generalized-alpha approach, respectively.
Open Access
Nonlinear dynamics of the tippedisk : a holistic analysis
(2023) Sailer, Simon; Leine, Remco I. (Prof. Dr. ir. habil.)
This dissertation deals with the tippedisk which is a new mechanical-mathematical archetype for friction-induced instabilities and exhibits an energetically counterintuitive inversion phenomenon. In a holistic analysis, the dynamics of the tippedisk is investigated numerically in the field of multibody simulation, theoretically in the field of nonlinear dynamics, and experimentally in the focus of applied physics. Based on different nonsmooth rigid body models with set-valued force laws, the main physical mechanisms inducing the inversion behavior are identified and the governing system equations are derived. Subsequent model reduction results in a reduced system in the form of an ordinary differential equation, which is suited to be studied in the context of nonlinear dynamics. Both the local stability behavior of the non-inverted and inverted stationary spinning motions as well as the global proof of an existing heteroclinic saddle connection allow the dynamic behavior of the tippedisk to be captured analytically. The particular structure of the mathematical model reveals a singularly perturbed dynamics that evolves on multiple time scales and is characterized by slow rolling and fast sliding motions of the tippedisk. Utilizing perturbation expansions and an analysis in dimensionless quantities, the qualitative dynamics is characterized by closed-form expressions, from which a global stability map is deduced. Based on this complete stability map, three different bifurcation scenarios are identified, which correspond to different geometric and inertia properties, defining three qualitatively different types of tippedisks. Finally, the mathematical investigation is complemented by high-speed experiments on a real test specimen. Qualitative comparison of experimental measurements with simulations at different levels of abstraction completes the holistic approach to the dynamic analysis of the tippedisk.
Open Access
Projected and partitioned Runge-Kutta methods for nonsmooth mechanical systems with frictional contact and impacts
(2024) Breuling, Jonas; Leine, Remco I. (Prof. Dr. ir. habil.)
Open Access
Stability and finite element analysis of fractionally damped mechanical systems
(2021) Hinze, Matthias; Leine, Remco I. (Prof. Dr. ir. habil.)
Open Access
State observers for mechanical systems with unilateral constraints : a discretization-based approach and experimental analysis
(2022) Preiswerk, Pascal V.; Leine, Remco I. (Prof. Dr. ir. habil.)
This monograph deals with the state observer design for mechanical systems with unilateral constraints. After the mathematical modeling is discussed in detail, necessary tools, which extend Lyapunov stability theory, are provided. A state observer design approach is investigated, which, in contrast to most existing observer designs, does not assume that closed contacts are instantaneously detected through measurements. In particular, a time discretization-based method is analyzed, which allows to circumvent some of the main difficulties caused by discontinuous time evolutions. Moreover, various state observer designs are implemented and tested on an experimental setup consisting of an impact oscillator.