By Dan B. Marghitu
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB presents an intensive, rigorous presentation of kinematics and dynamics whereas utilizing MATLAB as an built-in instrument to unravel difficulties. issues awarded are defined completely and directly,allowing basic ideas to emerge via functions from components equivalent to multibody platforms, robotics, spacecraft and layout of complicated mechanical units. This publication differs from others in that it makes use of symbolic MATLAB for either idea and functions. unique recognition is given to strategies which are solved analytically and numerically utilizing MATLAB. The illustrations and figures generated with MATLAB strengthen visible studying whereas an abundance of examples provide extra help.
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Additional info for Advanced Dynamics: Analytical and Numerical Calculations with MATLAB
Example text
RA(2)+rB(2))/2,... 5 x Fig. 3,... ’u’,’fontsize’,14,’fontweight’,’b’) xlabel(’x’), ylabel(’y’), zlabel(’z’) The MATLAB representation of the vectors is shown in Fig. 14. 3. The vectors V1 , V2 , V3 , and V4 with the magnitude |V1 | = V1 , |V2 | = V2 , |V3 | = V3 , and |V4 | = V4 are concurrent at the origin O(0, 0, 0) and are directed through the points of coordinates A1 (x1 , y1 , z1 ), A2 (x2 , y2 , z2 ), A3 (x3 , y3 , z3 ), and A4 (x4 , y4 , z4 ), respectively. Determine the resultant vector of the system.
5. The vector p of magnitude |p| = p is located in the x − z plane and makes an angle θ with x-axis as shown in Fig. 17a. The vector q of magnitude |q| = q is situated along the x-axis. Compute the vector (cross) product v = p × q. Numerical application: |p| = p = 5, |q| = q = 4, and θ = 30◦ . Solution The vector product v is perpendicular to the vectors p and q and that is why the vector v is along the y-axis and with has the magnitude |v| = |p| |q| sin θ = pq sin θ = 5(4) sin 30◦ = 10. From Fig.
If X and Y are second-order tensors with the components Xi j and Yi j , one can define ⇒ ⇒ ⇒ ⇒ ⇒ Z = X + Y= Y + X, as the arithmetic sum of the tensors. The previous equality is known as commutative law of addition. 4. The following properties can be written: Associative law of addition ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ X+ Y+Z = X+Y +Z. ⇒ ⇒ For every tensor X, there is a tensor − X such that ⇒ ⇒ ⇒ ⇒ X + − X = − X + X= 0. Commutative law of scalar multiplication ⇒ ⇒ λ X= X λ . Associative law of scalar multiplication ⇒ ⇒ ⇒ λ μ X = μ λ X = λμ X .