By L. I. Sedov, J. R. M. Radok
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Additional info for A course in continuum mechanics Vol. I Basic equations and analytical techniques
37 The resulted road in the global frame Fig. 38 Actual road (red) vs. 87) The equation for the steering angles has been found and illustrated in comparison with the kinematic steering angles in Fig. 35. As it can be seen in both Figs. 36, the difference between the two is very small in case of a slow forward velocity (vx D 1), and it happens mostly while returning to the straight section of the road. In order to validate the new method and the steering angles found using this method, the equation of motion of the vehicle was solved once again and this time by substituting the new steering angles found using the steady-state responses of the vehicle.
Au © Springer International Publishing Switzerland 2015 L. N. M. Harithuddin et al. Fig. 1 Three coordinate frames system A zA B zB zC C B yC yA yB xB xA xC coordinate frames. B D 0. One advantage of the general mixed derivative transformation formula is that it leaves the need to compute the derivative of B d B =dt in its local coordinate frame. An interesting result appears from the application of a reference frame system with three coordinate frames. A new acceleration term, given the name the Razi acceleration (Jazar 2011), is shown to appear when the derivatives of an acceleration vector are taken from two different coordinate frames.
T C 0:0277 cos. t 0:0743 sin. 46) 14 H. Marzbani et al. The global frame G is fixed on the ground, and B coincides with G at the start of maneuvers. The B-frame moves with the vehicle while the axes z and Z are always parallel. 50) 0 vY dt D 0 t t 0 When the steer angle is kept constant, the vehicle will eventually be turning on a constant circular path. 55) where G G rB is the G-expression of the position vector of the origin of the B-frame with respect to the origin of the G-frame at any point on the steady-state conditions (Jazar 2011).