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There are mainly two kinds of methods to model the unilateral constraints. The first kind is based on smooth contact dynamics, including methods using Hertz's models, penalty methods, and some regularization force models, while the second kind is based on the non-smooth contact dynamics, which models the system with unilateral contacts as variational inequalities.
A starting point for solving contact problems is to understand the effect of a "point-load" applied to an isotropic, homogeneous, and linear elastic half-plane, shown in the figure to the right. The problem may be either plane stress or plane strain. This is a boundary value problem of linear elasticity subject to the traction boundary conditions:
The elastic half-space problem is solved analytically, see the Boussinesq-Cerruti solution. Due to the linearity of this approach, multiple partial solutions may be super-imposed. Using the fundamental solution for the half-space, the full 3D contact problem is reduced to a 2D problem for the bodies' bounding surfaces.
Stiction (a portmanteau of the words static and friction) [1] is the force that needs to be overcome to enable relative motion of stationary objects in contact. [2] Any solid objects pressing against each other (but not sliding) will require some threshold of force parallel to the surface of contact in order to overcome static adhesion. [3]
The guards in rules are built-in constraints, so they effectively execute host language code. The built-in constraint theory must include at least true (the constraint that always holds), fail (the constraint that never holds, and is used to signal failure) and equality of terms, i.e., unification. [7]
The shaft and pulleys share a common centerline. The constraints of the key are set in relation to the keyseat. A constraint in computer-aided design (CAD) software is a limitation or restriction imposed by a designer or an engineer upon geometric properties [1]: 203 of an entity of a design model (i.e. sketch) that maintains its structure as the model is manipulated.
Inspired by—but distinct from—the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle. [2] Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian. [3]
Gimbal lock is the loss of one degree of freedom in a multi-dimensional mechanism at certain alignments of the axes. In a three-dimensional three-gimbal mechanism, gimbal lock occurs when the axes of two of the gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.