Ground Vehicle Dynamics by Karl Popp

By Karl Popp

Ground motor vehicle Dynamics is dedicated to the mathematical modelling and dynamical research of floor car platforms composed of the automobile physique, the tips and suspension units and the corresponding guideway. cars on asymmetric roads and railways on versatile tracks are well-liked representatives of floor automobile structures. these kind of other kinds of platforms are handled in a standard method by way of analytical dynamics and keep an eye on conception. as well as a close modelling of cars as multibody structures, the touch concept for rolling wheels and the modelling of guideways by way of finite aspect platforms in addition to stochastic strategies are provided. As a specific results of this built-in process the nation equations of the worldwide structures are received together with the full interactions among the subsystems regarded as autonomous modules. the basics of car dynamics for longitudinal, lateral and vertical motions and vibrations of vehicles and railways are mentioned in detail.

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2h (7) b) The computation of the trajectory of the bottle rR RK (t) in the vehiclefixed frame R, Fig. 13 b), means a transformation of the trajectory (5) from frame I to frame R. From Fig. 13 b) it follows 32 2 Vehicle Models ⎤ R sin γ r IR (t) = ⎣R(1 − cos γ)⎦ , 0 ⎡ r IRK (t) = r I (t) − rIR (t) , γ= vF t , R (8) where angle γ identifies the position of the vehicle on the circuit. The transformation law reads as RI I rR r RK (t) = S RI r I (t) − r IR (t) , RK (t) = S ⎤ ⎡ cos γ − sin γ 0 S RI = γ 3 = ⎣ sin γ cos γ 0⎦ .

28) This equation is valid for arbitrary vectors r and can be used as a general rule for the differentiation of vectors in different frames moving relative to each other. 28) means that the absolute variation 30 2 Vehicle Models ∗ dI /dt r(t) = r(t) (observed in the inertial frame I) consists of the relative ˙ variation dR /dt r(t) = r(t) (observed in the inertial frame R) supplemented by the rotation part ω IR (t) × r(t). Absolute and relative variation coincide only if the vector r is parallel to the angular velocity vector ω IR .

7) γ˙ − αβ˙ The evaluation of the rolling condition (5) neglecting all quantities which are small of higher order yields x˙ + aγ˙ − rl β˙ = 0 , ˙ =0, y˙ − rl (α˙ + γ β) (8) (9) z˙ − aα˙ = 0 , x˙ − aγ˙ − rr β˙ = 0 , ˙ =0, y˙ − rr (α˙ + γ β) (12) z˙ + aα˙ = 0 . (13) (10) (11) Equations (8) to (13) are related to the inertial frame. For a conical wheelset δ0 = 0 the vertical velocities (10) and (13) are depending on the roll angular velocity α. ˙ In the average of (10) and (13) it remains z˙ = 0 what is confirmed by the geometric relation (19).

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