Constraint (mechanics): Difference between revisions
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{{short description|Parameter which a physical system must obey}} |
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In classical mechanics, a '''constraint''' is a relation between coordinates and momenta (and possibly higher derivatives of the coordinates). |
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[[File:Friction angle.png|thumb|In this system the box slides down a slope, the constraint is that the box must remain on the slope (it cannot go through it or start flying).]] |
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In [[classical mechanics]], a '''constraint''' on a [[Physical system|system]] is a [[parameter]] that the system must obey. For example, a box sliding down a slope must remain on the slope. There are two different types of constraints: [[Holonomic constraints|holonomic]] and non-holonomic.<ref>{{Cite book|title=Molecular Modelling: Principles and Applications|last=Leach|first=Dr Andrew|date=2001-01-30|publisher=Prentice Hall|isbn=9780582382107|edition= 2nd|location=Harlow|pages=369–370|language=en}}</ref> |
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==Types of constraint== |
==Types of constraint== |
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*[[First class constraint]]s and [[second class constraints]] |
*[[First class constraint]]s and [[second class constraints]] |
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*[[Primary constraint]]s, [[secondary constraint]]s, [[tertiary constraint]]s, [[quaternary constraint]]s |
*[[Primary constraint]]s, [[secondary constraint]]s, [[tertiary constraint]]s, [[quaternary constraint]]s |
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*[[Holonomic |
*[[Holonomic constraints]], also called integrable constraints, (depending on time and the coordinates but not on the momenta) and [[Nonholonomic system]] |
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*[[Pfaffian constraint]]s |
*[[Pfaffian constraint]]s |
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*[[ |
*[[Scleronomic constraint]]s (not depending on time) and [[rheonomic constraint]]s (depending on time) |
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*Ideal constraints: those for which the work done by the constraint forces under a virtual displacement vanishes. |
*Ideal constraints: those for which the work done by the constraint forces under a virtual displacement vanishes. |
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==References== |
==References== |
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{{reflist}} |
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*{{Citation | last1=Goldstein | first1=Herbert | author1-link=Herbert Goldstein | last2=Poole | first2=Charles | last3=Safko | first3=John | title=Classical Mechanics | publisher=[[Addison-Wesley]] | edition=3rd | isbn=978-0-201-65702-9 | year=2002}} |
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[[Category:Classical mechanics]] |
[[Category:Classical mechanics]] |
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[[fa: دستگاههای مقید]] |
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{{classicalmechanics-stub}} |
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Latest revision as of 18:53, 3 January 2024
In classical mechanics, a constraint on a system is a parameter that the system must obey. For example, a box sliding down a slope must remain on the slope. There are two different types of constraints: holonomic and non-holonomic.[1]
Types of constraint
[edit]- First class constraints and second class constraints
- Primary constraints, secondary constraints, tertiary constraints, quaternary constraints
- Holonomic constraints, also called integrable constraints, (depending on time and the coordinates but not on the momenta) and Nonholonomic system
- Pfaffian constraints
- Scleronomic constraints (not depending on time) and rheonomic constraints (depending on time)
- Ideal constraints: those for which the work done by the constraint forces under a virtual displacement vanishes.
References
[edit]- ^ Leach, Dr Andrew (2001-01-30). Molecular Modelling: Principles and Applications (2nd ed.). Harlow: Prentice Hall. pp. 369–370. ISBN 9780582382107.
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