Satellites are free-moving rigid bodies subject to various external forces which make them deviate from their predetermined positional and rotational trajectories. Since many remote sensing imaging devices use the linear pushbroom scanning model, trajectory deviation during the image scanning period causes geometric distortion in the imagery. Unless actual satellite trajectory during imaging is modeled, accurate rectification of imagery is impossible. A means of recovering the trajectory from known satellite motion is presented here. Rotational motion is usually sensed by gyroscopes which measure angular velocity. Translational motion can be determined in several ways including telemetry analysis and linear accelerometers. In more recent satellites GPS receivers may be used to determine motion data. We show how to interpolate and subsequently integrate angular velocity to yield a rotational trajectory. The screw, implemented as a dual-number quaternion, is shown to be a suitable parameterization of motion to model the trajectory as a kinematic chain. This representation is useful for image geometry analysis and hence for correction of image distortion. Applications of this parameterization to scanned image resampling and rectification are mentioned.