Before revision: If the chaser satellite has mass and thrusters that apply a force then the relative dyanmics are given by the LTI control system where is the applied force per unit mass and Solution We can obtain closed form solutions of these coupled differential equations in matrix form, allowing us to find the position and velocity of the chaser at any time given the initial position and velocity.where:Note that and .
After revision: If the chaser satellite has mass and thrusters that apply a force then the relative dynamics are given by the LTI control system where is the applied force per unit mass and Solution We can obtain closed form solutions of these coupled differential equations in matrix form, allowing us to find the position and velocity of the chaser at any time given the initial position and velocity.where:Note that and .