The Physics of the Damped Harmonic OscillatorExplores 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 underdamping, overdamping, and critical damping.
打开实时脚本Validate Simulink Model Using Symbolic Math ToolboxModel 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 弹球的仿真 (Simulink).
打开实时脚本Derive and Apply Inverse Kinematics to Two-Link Robot ArmDerive and apply inverse kinematics to a
two-link robot arm by using MATLAB and Symbolic Math Toolbox.
打开实时脚本Gauss-Laguerre Quadrature Evaluation Points and WeightsSolve polynomial equations and systems of equations, and work with the results using Symbolic Math Toolbox™.
打开实时脚本Simulate a Stochastic Process Using the Feynman–Kac FormulaObtains the partial differential equation that describes the expected final price of an asset whose price is a stochastic process given by a stochastic differential equation.
打开实时脚本The Black–Scholes Formula for Call Option PriceCalculate the call option price using the Black–Scholes formula. This example uses vpasolve to numerically solve the problems of finding the spot price and implied volatility from the Black–Scholes formula.
打开实时脚本Heating of Finite SlabFind the temperature distribution of a one-dimensional finite slab by solving the
differential equation using the method of separation of variables.
打开实时脚本Derive Equations of Motion and Simulate Cart-Pole SystemDerive the equations of motion for the cart-pole system using Symbolic Math Toolbox™ and then simulate the cart-pole system using the ode45 solver. In the later sections of the example, you explore how to derive the equations in other forms that can be used to numerically simulate the system (and validate the results) using different tools, such as Simulink®, Simscape™ Multibody™, and Robotics System Toolbox™.
打开实时脚本Finite Element Formulation for Timoshenko Beam ProblemApply the finite element method (FEM) to solve a Timoshenko beam problem, using both linear and quadratic basis functions for analysis. The Timoshenko beam theory is a 1-D problem that reduces the complex 3-D problem of beam deformation to a set of 1-D differential equations along the length of the beam. In contrast to the Euler–Bernoulli beam theory, which does not consider shear deformation, the Timoshenko beam theory accounts for both shear deformation and rotational bending effects. The Timoshenko beam theory is generally more accurate for short, thick beams where shear deformation cannot be neglected. Using a cantilever beam and a beam fixed at both ends, this example discusses the analytical solutions of the Timoshenko beam problem and compares them with the FEM solutions.
打开实时脚本Analyze Transfer Function of T-Coil CircuitAnalyze the transfer function of a T-coil circuit using Symbolic Math Toolbox™ and Control System Toolbox™. In this example, you define symbolic equations, solve for the transfer function, and analyze the stability, frequency response, and step response of the circuit.
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