One of the interesting problems in dynamics of machines occurs when the appropriate coordinate system for describing the problem happens to moving, and not just moving but accelerating. This means that Newton’s Laws do not apply in that coordinate system, so suddenly things get complicated. That does not remove the need for answers, however.
One example of a moving coordinate system is such a system attached to a naval ship. Ships are often very large, but they are still subject to considerable accelerations due to the actions of winds and waves. Thus if we want to talk about the motion of shipboard equipment, we really need to consider this to be a situation of motion in an accelerated coordinate system.
The problem described in the attached PDF file falls into this category. It is one that came up some years ago, and I happened upon it in going through some old files a day or two ago. I thought I would share it with you.
I would like to invite those of you who are lurking out there to step forth out of the shadows and make a comment. I know that there is a modest group of you out there, but you are all very, very silent. I’d like to hear from you and get your feedback. Please feel free to leave a comment or ask a question on any of the posts.
Update 1: Well, wouldn’t you know it. I found an error in that write-up after I posted it. It will take a day or two to fix, but it will be back up shortly. Stay tuned!
Update 2: Now it is fixed and back up. It was a bigger problem than I realized at first, but it certainly needed to be fixed.
Tags: accelerated coordinates, Dynamics of Machines, Kinematics, Lagrange Equation, naval ship
