Continuous simulation
Encyclopedia
Continuous Simulation refers to a computer model of a physical system that continuously tracks system response over time according to a set of equations typically involving differential equations.
in 1946. Continuous simulation allows prediction of rocket trajectories, hydrogen bomb dynamics (N.B. this is the first use ever put to the Eniac
), electric circuit simulation, and robotics. Established in 1952, The Society for Modeling & Simulation (SCS) is a nonprofit, volunteer-driven corporation dedicated to advancing the use of modeling & simulation to solve real-world problems. Their first publication strongly suggested that the Navy was wasting a lot of money through the inconclusive flight-testing of missiles, but that the Simulation Councils analog computer could provide better information through the simulation of flights. Since that time continuous simulation has been proven invaluable in military and private endeavors with complex systems. No Apollo moon shot would have been possible without it.
stations, commercial flight simulators, jet plane auto pilots, and advanced engineering design tools. Indeed, much of modern technology that we enjoy today would not be possible without continuous simulation.
s.
Newton's 2nd law
, F = ma, is a good example of a single ODE continuous system. Numerical integration methods such as Runge Kutta, or Bulirsch-Stoer
are used to solve the system of ODEs. By coupling the ODE solver with other numerical operators and methods a continuous simulator can be used to model many different physical phenomena such as flight dynamics, robotics, automotive suspensions, hydraulics, electric power, electric motors, human respiration, polar ice cap melting, steam power plants etc. There is virtually no limit to the kinds of physical phenomena that can be modeled by a system of ODE's. Some systems though can not have all derivative terms specified explicitly from known inputs and other ODE outputs. Those derivative terms are defined implicitly by other system constraints such as Kirchoff's law that the flow of charge into a junction must equal the flow out. To solve these implicit ODE systems a converging iterative scheme such as Newton-Raphson must be employed.
History
It is notable as one of the first uses ever put to computers, dating back to the EniacENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
in 1946. Continuous simulation allows prediction of rocket trajectories, hydrogen bomb dynamics (N.B. this is the first use ever put to the Eniac
ENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
), electric circuit simulation, and robotics. Established in 1952, The Society for Modeling & Simulation (SCS) is a nonprofit, volunteer-driven corporation dedicated to advancing the use of modeling & simulation to solve real-world problems. Their first publication strongly suggested that the Navy was wasting a lot of money through the inconclusive flight-testing of missiles, but that the Simulation Councils analog computer could provide better information through the simulation of flights. Since that time continuous simulation has been proven invaluable in military and private endeavors with complex systems. No Apollo moon shot would have been possible without it.
Modern applications
Continuous simulation is found inside WiiWii
The Wii is a home video game console released by Nintendo on November 19, 2006. As a seventh-generation console, the Wii primarily competes with Microsoft's Xbox 360 and Sony's PlayStation 3. Nintendo states that its console targets a broader demographic than that of the two others...
stations, commercial flight simulators, jet plane auto pilots, and advanced engineering design tools. Indeed, much of modern technology that we enjoy today would not be possible without continuous simulation.
Mathematical theory
In continuous simulation, the continuous time response of a physical system is modeled using ODEOrdinary differential equation
In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s.
Newton's 2nd law
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
, F = ma, is a good example of a single ODE continuous system. Numerical integration methods such as Runge Kutta, or Bulirsch-Stoer
Bulirsch–Stoer algorithm
In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method,...
are used to solve the system of ODEs. By coupling the ODE solver with other numerical operators and methods a continuous simulator can be used to model many different physical phenomena such as flight dynamics, robotics, automotive suspensions, hydraulics, electric power, electric motors, human respiration, polar ice cap melting, steam power plants etc. There is virtually no limit to the kinds of physical phenomena that can be modeled by a system of ODE's. Some systems though can not have all derivative terms specified explicitly from known inputs and other ODE outputs. Those derivative terms are defined implicitly by other system constraints such as Kirchoff's law that the flow of charge into a junction must equal the flow out. To solve these implicit ODE systems a converging iterative scheme such as Newton-Raphson must be employed.
Other types of simulation
- Computer simulationComputer simulationA computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
- Process simulationProcess simulationProcess simulation is used for the design, development, analysis, and optimization of technical processes and is mainly applied to chemical plants and chemical processes, but also to power stations, and similar technical facilities.- Main principle :...
- Discrete event simulationDiscrete Event SimulationIn discrete-event simulation, the operation of a system is represented as a chronological sequence of events. Each event occurs at an instant in time and marks a change of state in the system...
- Instructional SimulationInstructional Simulation- Instructional simulation or virtual learning environment :An instructional simulation, also called an educational simulation, is a simulation of some type of reality but which also includes instructional elements that help a learner explore, navigate or obtain more information about that system...
- Social simulationSocial simulationSocial simulation is a research field that applies computational methods to study issues in the social sciences. The issues explored include problems in sociology, political science, economics, anthropology, geography, archaeology and linguistics ....