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 device to unravel difficulties. issues provided are defined completely and directly,allowing primary ideas to emerge via functions from parts reminiscent of 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. targeted consciousness is given to ideas which are solved analytically and numerically utilizing MATLAB. The illustrations and figures generated with MATLAB make stronger visible studying whereas an abundance of examples provide extra help.
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Additional resources for Advanced Dynamics: Analytical and Numerical Calculations with MATLAB
At the start, the variable is initialized to value startval and is incremented (or decremented when step is negative) by the value step for each iteration. The statement is repeated until var has incremented to the value endval. 283 The vector Vi can be written as Vi = Vix ı +Viy j +Viz k, i = 1, 2, 3, 4. The resultant of the system is R= (Rx )2 + (Ry )2 + (Rz )2 = ∑ Vix 2 + ∑ Viy 2 + ∑ Viz 2 . The direction cosines of the resultant are cos θx = ∑ Viy ∑ Vix ∑ Viz , cos θy = , cos θz = . 098 The negative value of cos θy signifies that the resultant has a negative component in the y direction.
Color’,’k’,’LineWidth’,2) quiver3(x_B,y_B,z_B, R(1),R(2),R(3),1,... ’Color’,’r’,’LineWidth’,3) quiver3(x_B,y_B,z_B, u_R(1),u_R(2),u_R(3),1,... ’Color’,’b’,’LineWidth’,4) quiver3(x_B,y_B,z_B, VC(1),VC(2),VC(3),1,... 1,... 1,... 1,... 1,... 1,... ’V_1 x V_2’,’fontsize’,14,’fontweight’,’b’) A rotated MATLAB drawing of the vectors is shown in Fig. 16b. 52 1 Vector Algebra a b 5 z 4 y O z 3 x p z q 2 θ 1 p 0 20 y pxq 10 y O 0 q 10 5 0 -10 x -5 x Fig. 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.
13a, the rectangular component of the vector F on the OA direction is f, with the magnitude |f| = f . The vector F acts at an angle β with the positive direction of the x-axis. Find the magnitude |F| = F of the vector F. Numerical application: f =20, α = 30◦ , and β = 60◦ . b 20 18 16 14 F y 12 F y a 10 A θ f 8 6 f 4 α β O Fig. 11 Examples 37 Solution The component of F on the OA direction is |F| cos θ = f . From Fig. 13, the angle θ of the vector F with the OA direction is θ = β − α = 60◦ −30◦ = 30◦.