Non-smooth mechanics is a modeling approach in mechanics which does not require the time evolutions of the positions and of the velocities to be smooth...

non-smooth dynamical systems (NSDS): Mechanical systems (Rigid body or solid) with Unilateral contact and Coulomb friction as we find in Non-smooth mechanics...

measuring instrument Non-smooth mechanics – Modeling approach in mechanics Rolling (metalworking) – Metal forming process Shock (mechanics) – Sudden transient...

Non-smooth Mechanics and Applications, CISM Courses and Lectures. Springer, Wien, 1988 Pfeiffer F., Foerg M. and Ulbrich H. Numerical aspects of non-smooth...

contact mechanics. In non-smooth method, unilateral interactions between bodies are fundamentally modelled by the Signorini condition for non-penetration...

below (Springer LNACM 35, 2008). See also the other references on non-smooth mechanics. There are approaches to automatically proving properties of hybrid...

adhesion Friction Acoustics Frictionless plane Galling Lateral adhesion Non-smooth mechanics Normal contact stiffness Stick-slip phenomenon Transient friction...

(France). He may also be considered as the father of non-smooth mechanics, a field of Solid Mechanics dealing with mechanical systems subjected to unilateral...

differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, M {\displaystyle M} , equipped with a closed nondegenerate differential...

quantum mechanics. Let ( M , L ) {\displaystyle (M,{\mathcal {L}})} be a mechanical system with configuration space M {\displaystyle M} and smooth Lagrangian...

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.: 3  Originally applied...

atlas; for instance, one can modify the identity map using a localized non-smooth bump. Then consider the new atlas { ( Φ − 1 ( U α ) , ϕ α ∘ Φ ) } α ∈...

mathematics, Nambu mechanics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon...

autonomous system is a dynamic equation on a smooth manifold. A non-autonomous system is a dynamic equation on a smooth fiber bundle Q → R {\displaystyle Q\to...

analytique. Lagrangian mechanics describes a mechanical system as a pair (M, L) consisting of a configuration space M and a smooth function L {\textstyle...

geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'....

Classical mechanics is a physical theory describing the motion of objects such as projectiles, parts of machinery, spacecraft, planets, stars, and galaxies...

International Centre for Mechanical Sciences. Udine. Italy. 1987. In Non Smooth Mechanics and Applications. Ed. J.J. Moreau, P.D. Panagiotopoulos. CISM Course...

Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid...

dimensionless friction factor f. The complexity of f, dependent on the mechanics of the boundary layer and the flow regime (laminar, transitional, or turbulent)...

Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of...

and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system...

generalises the phase space from Hamiltonian mechanics. A Poisson structure (or Poisson bracket) on a smooth manifold M {\displaystyle M} is a function...

supported smooth functions h {\displaystyle h} on ( a , b ) {\displaystyle (a,b)} , then f {\displaystyle f} is identically zero. Here "smooth" may be interpreted...

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. This can be divided into compressive and adhesive...

differentiable (differentiability implies continuity). Modern day quantum mechanics is sometimes seen as violating the principle, with its idea of discrete...

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, an object being pulled apart, such...

arg max are known as non-singular or regular points. With the last expression given in the introduction, softargmax is now a smooth approximation of arg...

In fluid mechanics, a splash is a sudden disturbance to the otherwise quiescent free surface of a liquid (usually water). The disturbance is typically...

Liouville's theorem. In Hamiltonian mechanics, the phase space is a smooth manifold that comes naturally equipped with a smooth measure (locally, this measure...