Vector Mechanics, Interpretation of Problem

[c.teixeira]

Hi there.

I am an Aerospave Engineering student, revisiting Vector Mechanics. My course recommended textbook is "Vector Mechanics of Enginners, from Beer and Johnston". However, I have been complemeting with another book - " Methods of Analytical Dynamics, from Meirovitch". This book, treats Analytical Mechanics, which is beyond the scoop of my course. However, I am just reading the chapters concerning Motion relative to Rotating frames of reference and Rigid Body Dynamics.

Now, the Meirovitrch textbook is way more theotytical. but I gave it a lot of time to correcclty interpert the subject. The thing is, sometimes, when I try to apply the Meivotich equations to the Beer and Jonhston multiple exercices, the results are incorrect! I feel rather frustrated, since I don't now why!

For example, in the attached file, there is on of those exercices I am refering.

If I assume there is a Reference Frame rotating with ω1, I can then compute the velocity and acceleration of point A correctly using the expressions given in the Meirovitch. (second attached file). In this case, the relative velocity of point A is ω2 * r.

However, if I imagine a Reference Frame Rotating with an angular velocity Ω = ω1 + ω2, then there would be no relative motion of the point A. The results(both the velocity and aceleration) using this rotating frame are incorrect. But, shouln't it work? I have carefully looked at the meirovith deductions, and I think it should!


Greatfull for any help!

Regards

 

[KataKoniK]

Dear student,

Thank you for sharing your experience with the two textbooks and your frustration with applying the equations in one to the exercises in the other. It is not uncommon for different textbooks to approach a topic in different ways, and this can sometimes lead to confusion when trying to apply concepts and equations from one to the other.

In this case, it seems that the two textbooks are using different reference frames and equations to describe the same situation. While both approaches may be correct, they may not always give the same results when applied to a specific problem. This could be due to different assumptions or simplifications made in each approach.

My suggestion would be to carefully review the equations and assumptions used in each textbook and try to understand the reasoning behind them. This will help you better understand when and how to apply each set of equations to a given problem. It may also be helpful to consult with your professor or a tutor for further clarification and guidance.

In addition, it is important to remember that in real-world engineering applications, there is often no single "correct" approach or set of equations. It is a matter of choosing the most appropriate method for the specific problem at hand.

I hope this helps and wish you the best of luck in your studies.