Dynamical system simulation: Difference between revisions

Revision as of 16:03, 1 June 2024

Latest revision as of 17:51, 23 February 2025

(4 intermediate revisions by the same user not shown)

Line 1:

{{distinguishfor|classical dynamics simulations|Dynamical simulation}}

{{short description|Computer modeling of time-varying behavior of a dynamical system}}

'''DynamicDynamical system simulation''' (or '''dynamic system simulation)''' is the use of a computer program to model the time-varying behavior of a [[dynamical system]]. The systems are typically described by [[ordinary differential equations]] or [[partial differential equations]]. A simulation run solves the state-equation system to find the behavior of the state variables over a specified period of time. The equation is solved through numerical integration methods to produce the transient behavior of the state variables. Simulation of dynamic systems predicts the values of model-system state variables, as they are determined by the past state values. This relationship is found by creating a model of the system.{{sfnp|Korn|2007|p=2}}

==Overview==

Line 17:

==Applications==

The first applications of computer simulations for dynamic systems was in the aerospace industry.{{sfnp|Klee|Allen|2016|p=xiii}} Commercial uses of dynamic simulation are many and range from nuclear power, steam turbines, 6 degrees of freedom vehicle modeling, electric motors, econometric models, biological systems, robot arms, mass-spring-damper systems, hydraulic systems, and drug dose migration through the human body to name a few. These models can often be run in [[real-time simulation|real time]] to give a virtual response close to the actual system. This is useful in [[process control]] and [[mechatronic]] systems for tuning the [[automatic control]] systems before they are connected to the real system, or for human training before they control the real system.

Simulation is also used in computer games and animation and can be accelerated by using a [[physics engine]], the technology used in many powerful [[computer graphics]] [[software]] [[computer program|programs]], like [[3ds Max]], [[Maya (software)|Maya]], [[LightWave 3D|Lightwave]], and many others to simulate physical characteristics. In computer animation, things like [[hair]], [[cloth]], [[liquid]], [[fire]], and [[wiktionary:particles|particles]] can be easily modeled, while the human [[animator]] animates simpler objects. Computer-based dynamic animation was first used at a very simple level in the 1989 [[Pixar]] [[short film]] ''Knick Knack'' to move the fake snow in the snowglobe and pebbles in a fish tank.

Simulation is also used in computer games and animation and can be accelerated by using a [[physics engine]], the technology used in many powerful [[computer graphics]] [[software]] [[computer program|programs]], like [[3ds Max]], [[Maya (software)|Maya]], [[LightWave 3D|Lightwave]], and many others to simulate physical characteristics. In computer animation, things like [[hair]], [[cloth]], [[liquid]], [[fire]], and [[wiktionary:particles|particles]] can be easily modeled, while the human [[animator]] animates simpler objects. Computer-based dynamic animation was first used at a very simple level in the 1989 [[Pixar]] [[short film]] ''Knick Knack'' to move the fake snow in the snowglobe and pebbles in a fish tank.

== Example of dynamic simulation ==

[[Image:TRUE_Procedural_Animation.gif|right|[[Piston motion equations]]|frame]]

This animation was made with a software [[system dynamics]], with a 3D modeler. The calculated values are associated with parameters of the rod and crank. In this example the crank is driving, we vary both the speed of rotation, its radius, and the length of the rod, the piston follows.

==See also==