Symbolic Computations in MATLAB
Symbolic Math Toolbox™ enables you to perform symbolic computations from the MATLAB® command line by defining a special data type — symbolic objects. Functions are called using the familiar MATLAB syntax and are available for integration, differentiation, simplification, equation solving, and other mathematical tasks. Symbolic computations augment the numeric capabilities of MATLAB. You can convert symbolic results to numeric results and use them outside Symbolic Math Toolbox.
Categories
- Symbolic Variables, Expressions, Functions, and Preferences
Create symbolic variables, expressions, functions, and set preferences
- Operators and Elementary Operations
Perform arithmetic, relational, and logical operations on symbolic objects
- Conversion Between Symbolic and Numeric
Convert symbolic data to numerics, convert numerics to symbolic objects
- Units of Measurement
Use physical units, converting units, checking unit consistency and compatibility
Featured Examples
The Physics of the Damped Harmonic Oscillator
Explores the physics of the damped harmonic oscillator by solving the equations of motion in the case of no driving forces. This example investigates the cases of under-, over-, and critical-damping.
Simulate the Motion of the Periodic Swing of a Pendulum
Solve the equation of motion of a simple pendulum analytically for small angles and numerically for any angle.
Evaluate Average Power Delivered by Wind Turbine
Compute the average power output of a wind turbine using Symbolic Math Toolbox™ and Statistics and Machine Learning Toolbox™. In this example, you define a parametric analytical expression that models the conversion of wind energy to turbine power. Then you evaluate the average power output by assuming that the wind speed follows a Weibull distribution.
Developing an Algorithm for Undistorting an Image
Develops a mathematical model using the Symbolic Math Toolbox™ to undistort an image and features a local function in the live script.
Electric Dipole Moment and Radiation Power
Finds the average radiation power of two attracting charges moving in an elliptical orbit (an electric dipole).
Validate Simulink Model Using Symbolic Math Toolbox
Model a bouncing ball, which is a classical hybrid dynamic system. This model includes both continuous dynamics and discrete transitions. It uses the Symbolic Math Toolbox™ to help explain some of the theory behind ODE solving in the Simulation of a Bouncing Ball.
Using Symbolic Mathematics with Optimization Toolbox Solvers
Use the Symbolic Math Toolbox functions jacobian and matlabFunction
to provide analytical derivatives to optimization solvers.
Analytical Model of Cantilever Truss Structure for Simscape
Find parameterized analytical expressions for the displacement of a joint of a cantilever truss structure in both the static and frequency domains.
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