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The vehicle–track interaction and the resulting dynamic response of the vehicle involve a number of complex nonlinear problems. Large vertical loads act through a small contact patch leading to very high contact pressures. Transverse loads acting through this contact induce a relative velocity between wheel and rail expressed in non-dimensional form as a creepage. The wheel and rail profiles determine the contact patch shape and affect the ability of the vehicle to run stably. If the yaw stiffness of the axles is too low, the vehicle will become unstable at a relatively low speed; conversely, if the yaw stiffness is too high, the curving behaviour will be adversely affected. The vehicle suspension, especially the secondary suspension, also affects the ride comfort of passengers. Finally, it is shown how the speed profiles of accelerating and decelerating trains can be calculated from basic assumptions about the train power, adhesion and rolling resistance.