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Solving Linear ODE Using Laplace Transforms 2008-08-16 08:48:44 How can we use Laplace transforms to solve ode? The procedure is bestillustrated with an example. Consider the ode This is a linear homogeneous ode and can be solved using standard methods. Let Y(s)=L[y(t)](s). Instead of solving directly for y(t), we derive anew equation for Y(s). Once we find Y(s), we inverse transformto determine y(t). The first step is to take the Laplace transform of Read more:Linear
The Inverse Laplace Transform 2008-08-16 08:46:15 The inverse Laplace transform of the function Y(s) is the uniquefunction y(t) that is continuous on [0,infty) and satisfiesL[y(t)](s)=Y(s). If all possible functions y(t) are discontinous onecan select a piecewise continuous function to be the inverse transform. We will use the notation or Li[Y(s)](t) to denote the inverse Laplace transform of Y(s). Determining the Inverse
Laplace Transform
The Laplace Transform of a Function 2008-08-16 08:45:42 The Laplace Transform
of a function y(t) is defined by if the integral exists. The notation L[y(t)](s) means take the Laplace transformof y(t). The functions y(t) and Y(s) are partner functions. Note that Y(s) is indeed only a function of s since the definite integral is with respect to t. Examples Let y(t)=exp(t). We have The integral converges if s>1. The functions exp(t) and 1/(
Transfer Function - Part 7 2008-08-16 08:40:32 STATE SPACE FROM TRANSFER FUNCTION MATLAB can find the state space representation directly from the transfer function in two ways. To find the state space representation of the system from the numerator and denominator of the transfer function in the form x' = Ax + Bu y = Cx + Du use MATLAB's tf2ss command: [A, B, C, D] = tf2ss(num,den) where num is the vector of the numerator polynomial
Transfer Function - Part 6 2008-08-16 08:39:54 BODE PLOT USING THE TRANSFER FUNCTION MATLAB’s bode command plots the frequency response of a system as a bode plot. The syntax for the bode plot function in MATLAB is: bode(transferfunction) where transferfunction is the name of the transfer function system. EXAMPLE Find bode plot of the frequency response of the system tutorial_tf using MATLAB: >
Transfer Function - Part 5 2008-08-16 08:39:21 IMPULSE RESPONSE USING THE TRANSFER FUNCTION MATLAB can also plot the impulse response of a transfer function. Because the transfer function is in the form of output over input, the transfer function must be multiplied by the magnitude of the impulse. The syntax for plotting the impulse response is: impulse(u * transferfunction) where u is the magnitude of the impulse and transferfu
Transfer Function - Part 4 2008-08-16 08:38:45 STEP RESPONSE USING THE TRANSFER FUNCTION Once the transfer function is entered into MATLAB it is easy to calculate the response to a step input. To calculate the response to a unit step input, use: step(transferfunction) where transferfunction is the name of the transfer function of the system. For steps with magnitude other than one, calculate the step response using: step(u * transferfunc
Transfer Function - Part 3 2008-08-16 08:38:04 HOW TO INPUT THE TRANSFER FUNCTION INTO MATLAB In order to enter a transfer function into MATLAB, the variables much be given numerical value, because MATLAB cannot manipulate symbolic variables without the symbolic toolbox. Enter the numerator and denominator polynomial coefficients separately as vectors of coefficients of the individual polynomials in descending order. The syntax for defin
Transfer Function - Part 2 2008-08-16 08:35:35 HOW TO FIND THE TRANSFER FUNCTION In most cases the governing equation will be linear, consisting of a variable and its derivatives. The Laplace Transform allows a linear equation to be converted into a polynomial. The most useful property of the Laplace Transform for finding the transfer function is the differentiation theorem. Several properties are shown below: Time
Applied Numerical Methods Using MatlaB 2008-08-16 03:20:28 y batoran-Applied Numerical Methods
Using MatlaB - Won Y Yang - Upload a Document to Scribd Read this document on Scribd: y batoran-Applied Numerical Methods Using MatlaB - Won Y Yang
MATLAB®Simulink® 6 6 2008-08-16 02:57:11 MATLAB®Simulink® 6 6 - Upload a Document to Scribd Read this document on Scribd: MATLAB®Simulink® 6 6
Introduction to Matlab 2008-08-16 02:54:01 Introduction to Matlab
- Upload a Document to Scribd Read this document on Scribd: Introduction to Matlab Read more:Introduction
MATLAB 2008-08-16 02:53:22 MATLAB - Upload a Document to Scribd Read this document on Scribd: MATLAB
Cramer's Rule 2008-08-14 15:14:44 Given a set of linear equations (1) consider the determinant (2) Now multiply by , and use the property of determinants that multiplication by a constant is equivalent to multiplication of each entry in a single column by that constant, so (3) Another property of determinants enables us to add a constant times any column to any column and obtain the same determina Read more:Cramer
Matrix Equation 2008-08-14 15:13:22 Nonhomogeneous matrix equations of the form (1) can be solved by taking the matrix inverse to obtain (2) This equation will have a nontrivial solution iff the determinant . In general, more numerically stable techniques of solving the equation include Gaussian elimination, LU decomposition, or the square root method. For a homogeneous matrix equation (3) to be Read more:Equation
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LU Decomposition 2008-08-14 15:11:16 A procedure for decomposing an matrix into a product of a lower triangular matrix and an upper triangular matrix , (1) LU decomposition is implemented in Mathematica as LUDecomposition[m]. Written explicitly for a matrix, the decomposition is (2) (3) This gives three types of equations (4) (5) j l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ij)u_(jj)=a_(ij). " wi
Gaussian Elimination 2008-08-14 15:08:41 Gaussian elimination is a method for solving matrix equations of the form (1) To perform Gaussian elimination starting with the system of equations (2) compose the "augmented matrix equation" (3) Here, the column vector in the variables is carried along for labeling the matrix rows. Now, perform elementary row operations to put the augmented matrix into the upper Read more:Elimination
Gauss Elimination - Numerical Method 2008-08-14 15:07:10 A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix[A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... |; a_(n1) ... a_(nn) 0 0 ... 1], (1)where I is the identity matrix, and use Gaussian elimination to obtain a matrix of the form[1 0 ... 0 b_(11) ... b_(1n); 0 1 ... 0 b_(21) ... b_(2n); | | ... | | ... |; 0 0 ... 1 b_(n1) ... Read more:Elimination
Precision Sheet Metal Fabrication 2008-08-10 23:00:08 Metal fabrication is a process of producing a metal component by modifying a raw piece of material in a machine shop. These materials are processed on different temperatures and depending on the range of temperatures; the process is classified as cold, warm and hot. Precision
sheet metal fabrication describes various different processes that form sheet metal into finished products. Objects that ar Read more:Metal
Internet Advertising vs. Conventional Advertising 2008-08-10 22:09:17 Conventional advertising could never be replaced. However, because of developments in the technology, people prefer their services online. With low cost internet advertising solutions present, the consumers, companies, advertisers and even the common people's Since the early 90's, the internet has become known as a medium for advertising. It has also been preferred by consumers and businessmen in Read more:Advertising
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Increasing Your Income Through Google AdSense 2008-08-10 22:05:43 Most webmasters know that Adsense generates a sizeable source of additional advertising income. That is why most of them use it to go after high paying keywords.They have with them the lists that tell what the keywords are and have already used various methods of identifying them. And yet, after putting up these supposed-to-be high paying keywords into their pages, the money they expected to come Read more:Google
, Income
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Solid Modeling 2008-09-01 16:14:00 A mathematical technique for representing solid objects. Unlike wireframe and surface modeling, solid modeling systems ensure that all surfaces meet properly and that the object is geometrically correct. Solid
models allow for interference checking, which tests to see if two or more objects occupy the same space.Solid modeling is the most complicated of the CAD technologies, because it simulates a Read more:Modeling
Alibre Design Xpress 3D Solid Modeler 2008-09-01 15:43:00 Alibre Design Xpress
is a rich and capable 3D solid modeler for creating mechanical parts, assemblies and 2D drawings - and is free. Certain more elegant features, like 3D sketching and part Booleans, can be found in the paid versions of the Alibre Design product family. Alibre Design Xpress equips the person needing basic 3D design capabilities. Easy to Use and LearnThe genius of Alibre Desi Read more:Solid
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