453 HW_1 - MAE 453: Introduction to Space Flight Department...

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MAE 453: Introduction to Space Flight Spring 2010 Department of Mechanical and Aerospace Engineering North Carolina State University Homework 1: Dynamics of point masses DUE DATE: 1/27/10 1. The x , y , and z coordinates (in meters) of a particle P as a function of time (in seconds) are x = sin t, y = sin 2t and z = sin 3t . At t = 3 seconds, determine: a) the velocity of the particle b) the speed of the particle c) the angles x , y and z which the velocity vector makes with the x, y and z axes d) the unit tangent vector e) the acceleration of the particle f) the unit binormal vector g) the unit normal vector h) the tangential component of the acceleration i) the normal component of the acceleration j) the radius of curvature of the path of P 2. At a given instant, the absolute position, velocity and acceleration of O are: ) / ( ˆ 15 ˆ 40 ˆ 25 ) / ( ˆ 50 ˆ 30 ˆ 10 ) ( ˆ 100 ˆ 200 ˆ 300 2 s m K J I a s m K J I v m K J I r O O O The angular velocity and acceleration of the moving frame are: ) / (
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453 HW_1 - MAE 453: Introduction to Space Flight Department...

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