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Journal Articles SIAM Journal on Control and Optimization Year : 1966

## Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints

Jean Jacques Moreau
• Function : Author

#### Abstract

Let $S$ be a frictionless mechanical system with $n$ degrees of freedom; we denote by $q_1,q_2,\ldots,q_n$ the generalized coordinates, representing the point $q$ of a configuration space. A finite family of one-sided constraints is imposed on the system; the kinematic effect of these constraints is expressed by the conditions (assumed compatible) $f_{\alpha}(q, t) \geq 0$, $\alpha \in I$, finite set of indexes. For instance, some solid parts of the system may be in contact or become detached but they can never overlap. These constraints are frictionless, i.e., as long as the equalities hold in the expression above, the motion of the system is governed by Lagrange's equations with multipliers $\lambda_{\alpha}$, $\alpha\in I$.

#### Domains

Engineering Sciences [physics] Mathematics [math]

### Dates and versions

hal-01379713 , version 1 (12-10-2016)

### Licence

Attribution - CC BY 4.0

### Identifiers

• HAL Id : hal-01379713 , version 1
• DOI :

### Cite

Jean Jacques Moreau. Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints. SIAM Journal on Control and Optimization, 1966, 4 (1), pp.153 - 158. ⟨10.1137/0304014⟩. ⟨hal-01379713⟩

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