## 1 Introduction
### The Literature Survey
They conclude that the curve radius is of unequivocal importance, the TC length is important provided the inflection point is not exceeded, superelevation is of minor importance (the differences in the results for the superelevation deficiency and excess are surprisingly small), and the CC length is of no importance at all. In [17], the authors focus on vibrations in passenger cars. They compare results from two approaches, one based on analytical solutions to dynamical equations and the other based on simulation, which means solving the equations numerically. Thanks to the greater DoFs possible and less simplification of the equations with the simulation approach, the authors conclude that it is superior to the other approach. The authors highlight the higher accuracy of the simulations. Publication [18] compares a few methods for nonlinear critical velocity determination. A simulation approach to this issue and ramping and path-following (continuation) methods are of primary interest. Different methods for hunting motion excitation are compared with each other in terms of the critical velocity value. The impact of the track class (its irregularities) on the results is also shown thanks to comparison with the results for an ideal track. In [19], the effect of the bogie's parameters in suspension on the lateral forces in the track frame is studied. This bogie is a three-piece traditional construction applied in freight cars. The authors consider 30 different bolster suspension combinations. It is concluded that an increase in the dumping force (the friction coefficient of the wedge) causes an increase in the lateral force of the track frame. Simultaneously increasing the bogie's lateral stiffness and the dumping force raises the lateral force of the track frame, too. On the other hand, the internal interplay between these two parameters also appears important. In [20], the hunting motion of a locomotive car body is studied experimentally and according to simulation. The aim is to explain and suggest measures to eliminate such hunting motion that appears for low conicity in wheel-rail contact. The measures concern the suspension parameters. Namely, the series stiffness and damping in the yaw damper and the longitudinal stiffness in the primary suspension are indicated as those that need to be decreased. Both ST and CC cases are analysed. In paper [21], the author studied interactions between a vehicle's internal elements and between the vehicle and the track to make sure that existing freight cars with three-piece bogies can run at higher permissible speeds under an increased axle load. ST and CC sections are considered. It is shown that such increases are possible. However, the bogies have to be replaced with slightly modernised ones. In [22], the authors propose a method to identify, rather than neglect, low-amplitude hunting in high-speed railway vehicles. They found that the coefficient of autocorrelation and the spread of spectral frequency are the most efficient parameters for this purpose. The findings are dedicated to supporting the monitoring of hunting motion instability and active control studies for high-speed trains in real time. Paper [23] is a general paper on the instability of limit-cycle-type oscillations. The aim is to derive an efficient computational method for instability modelling and handling hundreds, sometimes thousands, of design variables. This is fulfilled by using a simple metric to determine the stability of the limit cycle utilising a fitted bifurcation diagram slope. Stability derivatives for many design variables are efficiently computed using the developed adjoint-based formula. Publication [24] proposes a nonlinear wheel-rail kinematics model, which extends [PERSON]'s well-known linear model. The nonlinear model comprises high-order odd harmonic frequencies (HOHFs) [24], besides the basic hunting frequency. Along with this, HOHFs are sources of self-exciting vibrations in rail vehicles.