Trajectory planning and control in field robotics rely on predicting how propulsion and steering affect vehicle motion when contact points undergo slip. For articulated vehicles, the point-contact kinematic model (PCK) accounts for the linkage geometry but neglects the rotational resistance distributed along the contacts. We propose a finite-support quadratic model (FSQ) for single-track, center-articulated vehicles that incorporates this resistance through a quasi-static balance of lateral slip. Our approach generalizes the standard PCK formulation by relaxing the contact-point assumption. An exact reduction of the quadratic slip cost to contact moments gives a compact closed-form solution for real-time prediction of lateral velocity and yaw rate. We evaluate the proposed method in real-world experiments across asphalt, grass, ice, and mixed routes, using more than 7 km of data. For five-second predictions, FSQ reduces the weighted median translation and yaw errors by 53.5% and 68.9%, respectively, relative to PCK.

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