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- Nonholonomic_system abstract "A nonholonomic system in physics and mathematics is a system whose state depends on the path taken to achieve it. Such a system is described by a set of parameters subject to differential constraints, such that when the system evolves along a path in its parameter space (the parameters varying continuously in values) but finally returns to the original set of values at the start of the path, the system itself may not have returned to its original state.More precisely, a nonholonomic system, also called an anholonomic system, is one in which there is a continuous closed circuit of the governing parameters, by which the system may be transformed from any given state to any other state. Because the final state of the system depends on the intermediate values of its trajectory through parameter space, the system can not be represented by a conservative potential function as can, for example, the inverse square law of the gravitational force. This latter is an example of a holonomic system: path integrals in the system depend only upon the initial and final states of the system (positions in the potential), completely independent of the trajectory of transition between those states. The system is therefore said to be integrable, while the nonholonomic system is said to be nonintegrable. When a path integral is computed in a nonholonomic system, the value represents a deviation within some range of admissible values and this deviation is said to be an anholonomy produced by the specific path under consideration. This term was introduced by Heinrich Hertz in 1894.The general character of anholonomic systems is that of implicitly dependent parameters. If the implicit dependency can be removed, for example by raising the dimension of the space, thereby adding at least one additional parameter, the system is not truly nonholonomic, but is simply incompletely modeled by the lower-dimensional space. In contrast, if the system intrinsically can not be represented by independent coordinates (parameters), then it is truly an anholonomic system. Some authors[citation needed] make much of this by creating a distinction between so-called internal and external states of the system, but in truth, all parameters are necessary to characterize the system, be they representative of "internal" or "external" processes, so the distinction is in fact artificial. However, there is a very real and irreconcilable difference between physical systems that obey conservation principles and those that do not. In the case of parallel transport on a sphere, the distinction is clear: a Riemannian manifold has a metric fundamentally distinct from that of a Euclidean space. For parallel transport on a sphere, the implicit dependence is intrinsic to the non-euclidean metric. The surface of a sphere is a two-dimensional space. By raising the dimension, we can more clearly see the nature of the metric, but it is still fundamentally a two-dimensional space with parameters irretrievably entwined in dependency by the Riemannian metric.".
- Nonholonomic_system wikiPageExternalLink macar2000-02.pdf.
- Nonholonomic_system wikiPageID "554248".
- Nonholonomic_system wikiPageRevisionID "604224310".
- Nonholonomic_system hasPhotoCollection Nonholonomic_system.
- Nonholonomic_system subject Category:Algebraic_topology.
- Nonholonomic_system subject Category:Classical_mechanics.
- Nonholonomic_system subject Category:Differential_geometry.
- Nonholonomic_system subject Category:Differential_topology.
- Nonholonomic_system subject Category:Physical_systems.
- Nonholonomic_system type Artifact100021939.
- Nonholonomic_system type Instrumentality103575240.
- Nonholonomic_system type Object100002684.
- Nonholonomic_system type PhysicalEntity100001930.
- Nonholonomic_system type PhysicalSystems.
- Nonholonomic_system type System104377057.
- Nonholonomic_system type Whole100003553.
- Nonholonomic_system comment "A nonholonomic system in physics and mathematics is a system whose state depends on the path taken to achieve it.".
- Nonholonomic_system label "Nonholonomic system".
- Nonholonomic_system label "Układ nieholonomiczny".
- Nonholonomic_system label "Неголономная система".
- Nonholonomic_system label "非ホロノミック系".
- Nonholonomic_system label "非完整系統".
- Nonholonomic_system sameAs 非ホロノミック系.
- Nonholonomic_system sameAs Układ_nieholonomiczny.
- Nonholonomic_system sameAs m.02pd1v.
- Nonholonomic_system sameAs Q2478109.
- Nonholonomic_system sameAs Q2478109.
- Nonholonomic_system sameAs Nonholonomic_system.
- Nonholonomic_system wasDerivedFrom Nonholonomic_system?oldid=604224310.
- Nonholonomic_system isPrimaryTopicOf Nonholonomic_system.