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DYNAMICS - CASE STUDY

    Introduction


Problem Graphic - Skew View


Problem Graphic - Side View

 

The designers of an attack sub are predicting its performance during dive maneuvers. When designing the coning tower, they must determine its contribution to the angular momentum about the center of gravity of the sub.

What is known:

  • At the instant the dive commences, the components of the velocity and angular velocity of the sub relative to the earth are
         vXI, vYJ, wYJ, -wXK (vZK = wZK = 0).
  • The dimensions of the sub and the coordinate system for the sub and the earth are shown in the diagram.
   
  Question

 

At the instant the dive commences, what are the inertial properties of the coning tower about the center of gravity of the sub?

At that same instant, what is the angular momentum of the coning tower about the center of gravity of the sub?

     

Problem Diagram

   
    Approach

   
  • Model the con as a homogeneous rectangular prism. Determine the inertial properties of the con about its center of gravity, then transfer them to the center of gravity of the sub.
  • Use the inertial properties of the con about the center of gravity of the sub to determine the angular momentum of the con about the center of gravity of the sub.
     
   
 
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