Homework 3 1. The rigid motion in one-dimensional space is characterized by the change of the angular momentum by addition of a torque. where is the moment of inertia, w is the angular velocity, and is a torque. This model is extended to the rigid body motion in three-dimensional space. In three-dimensional space, the rigid motion is characterized by the angular velocity components in three orthogonal directions X = T. where is the moment of inertia tensor, w is the angular velocity, and is the torque vector. If I is taken along the principales of the body, then it becomes diagonal Note that the expression in Equation (2) is described in the body frame each is is along the principal axis of the body). Also, in this analysis, we do not track the orientation of the body but only consider the angular velocity of it for simplicity. Here, 5.3 0 0 1 I= 0 740 kg m) 0 0 10.5 Answer the following questions (a) First, consider the dynamics of the system without linearizing Equation (2). De velop an RK4 scheme to solve this equation 1. As the initial condition, set w = 10.1.0.2.0.3 rad/sec). Compute the angular velocity at 10 sec. No torque is given in this case. ii. As the initial condition, set w = 10.2.0.1,0.5" (rad/sec) angular velocity at 1,000 sec. No torque is given in this case Compute the DX10-1 EX 10-2 ii. As the initial condition, set -2.0.0.5.10T /sec) Compute the angular velocity at 100,000 sec. No torque is given in this case iv. As the initial condition, set = 0.1,0.2, 0.3 rad/sec). Also, consider that the spacecraft experiences thrust continuously with a torque of 0.01 -0.01,0.01" (Nm). Compute the angular velocity at 100 sec. Homework 3 1. The rigid motion in one-dimensional space is characterized by the change of the angular momentum by addition of a torque. where is the moment of inertia, w is the angular velocity, and is a torque. This model is extended to the rigid body motion in three-dimensional space. In three-dimensional space, the rigid motion is characterized by the angular velocity components in three orthogonal directions X = T. where is the moment of inertia tensor, w is the angular velocity, and is the torque vector. If I is taken along the principales of the body, then it becomes diagonal Note that the expression in Equation (2) is described in the body frame each is is along the principal axis of the body). Also, in this analysis, we do not track the orientation of the body but only consider the angular velocity of it for simplicity. Here, 5.3 0 0 1 I= 0 740 kg m) 0 0 10.5 Answer the following questions (a) First, consider the dynamics of the system without linearizing Equation (2). De velop an RK4 scheme to solve this equation 1. As the initial condition, set w = 10.1.0.2.0.3 rad/sec). Compute the angular velocity at 10 sec. No torque is given in this case. ii. As the initial condition, set w = 10.2.0.1,0.5" (rad/sec) angular velocity at 1,000 sec. No torque is given in this case Compute the DX10-1 EX 10-2 ii. As the initial condition, set -2.0.0.5.10T /sec) Compute the angular velocity at 100,000 sec. No torque is given in this case iv. As the initial condition, set = 0.1,0.2, 0.3 rad/sec). Also, consider that the spacecraft experiences thrust continuously with a torque of 0.01 -0.01,0.01" (Nm). Compute the angular velocity at 100 sec
