By Dan B. Marghitu
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB offers an intensive, rigorous presentation of kinematics and dynamics whereas utilizing MATLAB as an built-in device to resolve difficulties. themes provided are defined completely and directly,allowing basic ideas to emerge via functions from components resembling multibody platforms, robotics, spacecraft and layout of advanced mechanical units. This ebook differs from others in that it makes use of symbolic MATLAB for either thought and functions. specific awareness is given to recommendations which are solved analytically and numerically utilizing MATLAB. The illustrations and figures generated with MATLAB strengthen visible studying whereas an abundance of examples supply extra help.
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The matrix attached to a tensor of rank two in a Cartesian reference frame Oxyz can be written as ⎛ ⎞ X11 X21 X31 X = ⎝ X12 X22 X32 ⎠ , X13 X23 X33 28 1 Vector Algebra and in the Cartesian reference frame, Ox y z is ⎛ ⎞ X11 X21 X31 X = ⎝ X12 X22 X32 ⎠ . 56), it is obtained X = A−1 X A. 55). Let X = (X1 , X2 , X3 ) and Y = (Y1 ,Y2 ,Y3 ) be two nonzero vectors written in a Cartesian reference frame Oxyz. The components Zi j = XiY j (i = 1, 2, 3 and j = ⇒ 1, 2, 3) define in the Cartesian reference frame Oxyz a tensor Z .
Thus (because A is an orthogonal matrix), det A = 1. 10 Tensors Let Oxyz and Ox y z be two sets of rectangular Cartesian reference frames. 45) as Xi = 3 ∑ αi j X j j=1 and Xi = 3 ∑ αi j X j , where i = 1, 2, 3. 53) where Xk (k = 1, 2, 3) are the components of a vector X. There are nine scalars X11 , X12 , X13 , X21 , X22 , X23 , X31 , X32 , and X33 . A vector defined in the Euclidean space has three components and is called a tensor of rank one. A tensor of rank two, in a Cartesian reference frame Oxyz, is a mathematical entity with nine components Xi j (i = 1, 2, 3 and j = 1, 2, 3).
Cos θ cos 30◦ The MATLAB program starts with the following statements: clear all % clears all the objects in the MATLAB workspace and % resets the default MuPAD symbolic engine clc % clears the command window and homes the cursor close all % closes all the open figure windows The MATLAB commands for the input data are f = 20; alpha = pi/6; beta = pi/3; The angle θ and the magnitude of the vector F are calculated with theta = beta-alpha; F = f/cos(theta); The statement cos(s) is the cosine of the argument s in radians.
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB by Dan B. Marghitu