fig1 shows a schematic block diagram of different vehicle safety systems , which are operated taking an estimated future rotary movement of the vehicle into account . the system includes an electronic stability control 1 , which is able to intervene in the driving operation via one or more actuators such as the vehicle brakes , for instance , in order to stabilize the vehicle . the associated actuators of electronic stability control 1 are combined here in a block 4 . the instantaneous driving situation is monitored with the aid of sensors 2 and 3 . as a rule , these are specifically a yaw rate sensor 2 and additional sensors , e . g ., wheel - speed sensors , steering - angle sensors and transverse acceleration sensors , which have been subsumed under number 3 in the figure . further sensors may be provided in addition , depending on the system . controller 1 estimates sideslip angle β of the vehicle in the known manner and forwards this value and also the value of the instantaneous yaw rate dpsi / dt to a unit 5 , which includes a mathematical model that estimates information about the future rotary movement of the vehicle therefrom . the sideslip angle prognosis in this case is based on a change in the yaw angle , which is predicted on the basis of the measured yaw rate . in the exemplary embodiment shown , the information estimated by unit 5 is a maximum sideslip angle β max , but it may also be any other item of information such as the course of the future rotary movement , for instance . the model included in unit 5 determines the future rotary movement while taking specific physical situations into account , especially the friction situation between tire and road , and preferably also assuming a specific intervention of vehicle control 1 . for the abating of a rotary movement ( taking the mentioned variables into account ), a parabolic function , for instance , may be used , which approximates the course of the yaw rate relatively well . in this case the following applies for yaw rate dpsi / dt : dpsi / dt = a 1 · t 2 + a 2 * t + a 3 , ( 1 ) a 1 , a 2 and a 3 being parameters and t being the time . preferably used as start value a 3 is the instantaneous measured value of yaw rate dpsi / dt . consequently : yaw angle psi results from a time integration of yaw rate ( 1 ) as : psi ( t )= int ( dpsi / dt ) dt + psi 0 = ⅓ · a 1 · t 3 + ½ a 2 · t 2 + a 3 · t + psi 0 ( 2 ) for the method it is assumed that ≈− psi is true for sideslip angle β , i . e ., that the sideslip angle thus roughly corresponds to the yaw angle in its amount . thus , it is preferred to use the instantaneous negative measured or estimated value of sideslip angle − β 0 for the start value psi 0 of the yaw angle . as a consequence , the following applies : the yawing acceleration may be estimated , for instance , from the tire forces and via the moment equilibrium d 2 psi / dt 2 = mz / j , mz being the highest yawing moment mz max ( β 0 ) achievable by brake and steering interventions as a function of the sideslip angle , and j being the mass moment of inertia . thus , the following holds for coefficient a 2 in equation ( 1 ): d 2 psi / dt 2 ( t = 0 )= a 2 = mz max ( β 0 ). in the course of the driving maneuver the estimation of the maximum sideslip angle is able to be improved by determining the instantaneous yawing acceleration on the basis of the measured yaw rate values . thus , only parameter a 1 is still undetermined in equation ( 1 ). one possibility for establishing parameter a 1 consists of determining it as a multiple of a 2 . thus , for instance , may be specified . instead of exemplary value 0 . 85 , it is also possible to specify a different value . this takes into account that the yawing moment able to be produced by electronic stability control 1 is greater at the beginning of a critical driving situation , in which the sideslip angle is small , than at greater sideslip angles , in which braking and also steering interventions no longer have more than a very negligible effect on the yawing motion . therefore , all coefficients from equation ( 1 ) are determined . the maximum sideslip angle is reached once the yaw rate has become zero , i . e ., when the following applies : for the instant at which the maximum sideslip angle occurs , two solutions are obtained from equation ( 1 ): t end1 = ½ / α 1 ·(− α 2 −( α 2 − 4 · α 1 · α 3 ) 1 / 2 ) ( 4a ) t end2 = ½ / a 1 ·(− a 2 +( a 2 − 4 · a 1 · a 3 ) 1 / 2 ) ( 4b ) finally , maximum yaw angle psi end results from equation 2 for t = t end . psi end = ⅓ · a 1 · t end 3 + ½ · a 2 · t end 2 + a 3 · t end − β 0 , and from this , the missing maximum sideslip angle β max as : maximum sideslip angle β max calculated in this manner is then able to be supplied to the electronic stability control , for instance , in order to control it as a function of the situation . for example , if the model - based estimation of the future rotary movement indicates that the vehicle would slide transversely for a longer period of time even with a full intervention of the vehicle stability program , then the actuating intervention of the vehicle stability program may be reduced to such an extent , for example , that the vehicle rotates further than 90 ° and the rotation comes to a stop at 180 °, for instance . this results in a considerably lower risk of a critical side impact for the passengers . knowledge of maximum sideslip angle β max may also be used to prepare a restraining system 6 for a potential collision . as an alternative , a driver assistance system 7 may also initiate emergency braking . fig2 a shows the curve of the yawing acceleration of a vehicle for which a side collision has occurred at the tail end and which therefore executes a rotary movement about the vertical axis of the vehicle . as can be gathered , the yawing acceleration as a result of the side collision first assumes a large positive value , so that the yaw rate in fig2 b rises rapidly . if the collision has come to an end , the yawing acceleration becomes negative due to friction and the intervention of electronic stability control 1 , and the yaw rate decreases again . fig2 b shows the curve of the associated yaw rate of the vehicle . as can be seen , it increases until a maximum has been reached after approximately 1 . 45 s . then , yaw rate dpsi / dt decreases continuously , that is to say , the rotary movement slows . fig2 c shows the curve of yaw angle 10 and simulation result 11 of the yaw angle prediction . as can be gathered , maximum yaw angle ψ max to be expected is able to be predicted very well starting already at the instant at which maximum yaw velocity dpsi / dt has been reached . it roughly corresponds to negative maximum sideslip angle β max , as explained above . as a consequence , vehicle control systems and / or restraining systems are already able to be adjusted according to the situation in a very timely manner .