The general form of the equations of motion of multi-axle railway vehicles are used to establish the conditions which the elastic stiffness matrix (which describes the nature and configuration of the suspension elements connecting the wheelsets) must satisfy in order to achieve perfect steering on curves, an adequate margin of stability and optimal response to cant deficiency. These conditions are illustrated by application to the most general form of symmetric three-axle vehicle and it is shown that an adequate margin of stability can be obtained for an optimized set of parameters which allows perfect linear curving. The class of configurations studied allows for unequal wheelset conicities and interwheelset assymmetry within the assumption of overall vehicle symmetry.

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