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Unformatted text preview: ME 131 Vehicle Dynamics Homework 2 Due Tuesday, February 23rd, 2010 1 Definitions and Concepts a. Define Cornering Stiffness (1 pt) b. Define the understeer gradient. (1 pt) d. An understeering vehicle is generally more stable than a neutral or oversteering vehicle. When is stability in a passenger vehicle undesirable? (1 pt) 2 Understeer, Oversteer, and Eigenvalues From page 31 of Rajamani, we can see the equations of lateral motion and yaw angle. d dt ˙ y ˙ ψ = "- (2 C αf +2 C αr ) mV x- V x- (2 C αf l f- 2 C αr l r ) mV x- (2 l f C αf- 2 l r C αr ) I z V x- (2 l 2 f C αf +2 l 2 r C αr ) I z V x # ˙ y ˙ ψ + " 2 C αf m 2 l f C αf I z # δ (1) This can also be represented as ˙ x = Ax + B δ (2) Assume all parameters are fixed except for the cornering stiffness of the front and rear tires. a. Using eigenvalue analysis, find the condition necessary for stability (5 pts). Major Hint: A linear system is stable if its eigenvalues have no positive real parts. To find the eigenvaluesMajor Hint: A linear system is stable if its eigenvalues have no positive real parts....
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This document was uploaded on 02/03/2011.
- Spring '09