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1. Generalized Coordinates

   Linked via "constraints"

   Generalized coordinates ($\mathbf{q}$) are a set of independent parameters used to uniquely specify the configuration of a mechanical system at any given instant. They form the basis of Lagrangian mechanics ($L$), offering a powerful alternative to the use of Cartesian coordinates, especially when dealing with systems subject to constraints. The number of generalized coordinates required to describe a system is equal to its degrees of freedom ($N_f$), which is calculat…

2. Mathematical Model

   Linked via "constraints"

   Conceptual Foundations and Axiomatics
   The foundation of any mathematical model/) rests upon a set of predefined axioms and constraints. In classical physics, these might derive from conservation laws (e.g., conservation of energy, momentum). In social sciences, the axioms are often derived from [behavioral assumptions](/entries/behavioral-assum…

3. Model

   Linked via "constraints"

   Computational Models and Simulation
   In computation, a model is typically a set of mathematical functions, parameters, and constraints instantiated within software. These computational constructs are fundamental to fields ranging from meteorology to finance.
   Force Field Modeling in Molecular Dynamics