Constrained Motion. In some cases a particle is forced to move along a curve or surface. This curve or surface is referred to as a constraint, and the resulting motion is called constrained motion. The particle exerts a force on the constraint, and by Newton's third law the constraint exerts a force on the particle.
https://people.maths.bris.ac.uk/~marrk/Mech/9_10_Projectiles...

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Constrained motion of a particle on an elliptical path
In Section 2 we discuss the motion of a constrained particle on an ellipse within the framework of the standard approach and the Dirac approach.
https://www.sciencedirect.com/science/article/pii/S181538521...
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An Introduction to Physically Based Modeling:
Constrained Dynamics
The idea of constrained particle dynamics is that our description of the system
https://www.cs.cmu.edu/~baraff/pbm/constraints.pdf
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One or more of the particles may each be subject to one or more holonomic constraints; such a constraint is described by an equation of the form f(r, t) = 0. If the number of constraints in the system is C, then each constraint has an equation, f1(r, t) = 0, f2(r, t) = 0, ... fC(r, t) = 0, each of which could apply to any of the particles. If particle k is subject to constraint i, then fi(rk, t) = 0. At any instant of time, the coordinates of a constrained particle are linked together and not independent. The constraint equations determine the allowed paths the particles can move along, but not where they are or how fast they go at every instant of time. Nonholonomic constraints depend on the particle velocities, accelerations, or higher derivatives of position. Lagrangian mechanics can only be applied to systems whose constraints, if any, are all holonomic. Three examples of nonholonomic constraints are:[11] when the constraint equations are nonintegrable, when the constraints have inequalities, or with complicated non-conservative forces like friction. Nonholonomic constraints require special treatment, and one may have to revert to Newtonian mechanics, or use other methods.
https://www.proz.com/kudoz/polish-to-english/physics/6703648...

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Note added at 13 mins (2019-09-02 14:16:19 GMT)
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really: https://en.wikipedia.org/wiki/Lagrangian_mechanics

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Also
Polish term or phrase: układ nieswobodny
English translation: constrained system
Entered by: Polangmar
https://www.proz.com/kudoz/polish-to-english/mechanics-mech-...
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punkt materialny nieswobodny
rzeczownik
constrained particle
https://www.diki.pl/slownik-angielskiego?q=punkt materialny ...
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