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This section tries to be relatively brief and condense links to some useful mathematical functions used in the articles by providing worked examples.
Two or More Degree of Freedom Systems:
Some useful notes to perform calculations on resonant frequencies, amplitudes etc. Click on image to download notes.
State Space:
More information: State-space_representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a vector within that space.
To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. The state-space method is characterized by significant algebraization of general system theory, which makes it possible to use Kronecker vector-matrix structures. The capacity of these structures can be efficiently applied to research systems with modulation or without it. The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs.
Taylor Series Linear Approximation:
more information: Reading Univ Taylor Series
Laplace Transform:
More information: Mass Spring Oscillator , Examples , Solving equations using Laplace (Colorado University)
fmincon Non-linear programming solver
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