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We examine the feasibility of designing an accelerometer-based (or gyroscope-free) inertial navigation system that uses only accelerometer measurements to compute the linear and angular motions of a rigid body. The accelerometer output equation is derived to relate the linear and angular motions of a rigid body relative to a fixed inertial frame. A sufficient condition is given to determine if a configuration of accelerometers is feasible. If the condition is satisfied, the angular and linear motions can be computed separately using two decoupled equations of an input-output dynamical system: a state equation for angular velocity and an output equation for linear acceleration. This simple computation scheme is derived from the corresponding dynamical system equations for a special cube configuration for which the angular acceleration is expressed as a linear combination of the accelerometer outputs. The effects of accelerometer location and orientation errors are analyzed. Algorithms that identify and compensate these errors are developed.