4 ms·

I never said it was advanced mechanics, what I said was it's not an introductory book. You shouldn't give this to someone who's never taken a physics course. It

I never said it was advanced mechanics, what I said was it's not an introductory book. You shouldn't give this to someone who's never taken a physics course. It's written for use in vehicle and aeronautical/astronautical dynamics and supposes a fairly developed understanding of coordinate systems and vector math. > Perhaps we have different definitions of "straightforward" It is certainly more straightforward than Lagrange. You just set up the constraints, which is done in two steps: (1) set up the kinematics, i.e. setting the position equal to some parameterization of that curve (2) set up the dynamics, i.e. express Newton's laws in terms of the same variables. After that, you can perform any derivatives needed using the transport theorem and set the kinematics and dynamics equal to each other using the common variables. > Coordinate invariance in physics means Since I'm not invoking the phrase "coordinate invariant" here I don't know what the deal is. All I said was that the concepts in this book express various physical laws including friction, Hooke's, and gravitational without use of coordinates. There is no X, Y, Z or 1, 2, 3 of the vectors in these descriptions. Whether to you that means coordinate invariant, is another story but ultimately irrelevant. > I still stand by the claim that this book is a pretty elementary one Considering you've spent all this time arguing that it's not straightforward (it is), I really suggest you take a look. It's nonconventional and may change your perspective if you really give it a chance.

b215826 7y ago
> Considering you've spent all this time arguing that it's not straightforward (it is), I really suggest you take a look. I just downloaded a copy of the book from LibGen. I change my original assessment that it might be a good introductory book. In fact, now I think that this is a terrible book that reinvents the wheel in so many places, and novices should avoid it since it teaches bad practices. E.g., look at Example 3-2 of the book where the task is to find the motion of the particle constrained on a parabola y = r^2/2R (similar to the paraboloid example I asked, but more easier since the constraint manifold is one-dimensional). The solution of that problem (Eq. 3-105) is 4 pages of algebra! The Lagrangian for the system expressed in terms of r is L = m/2*(1 + r^2/R^2)*v^2 - (mg/2R)*r^2, v being dr/dt. Now, to find Eq. 3-105, which the author derives in 4 pages, all it takes is to plug this Lagrangian into the Euler-Lagrange equations, and answer pops out in 2-3 lines of algebra involving some very trivial partial derivatives. Curiously, the author has also reinvented d'Alembert's principle when he does this problem the second time in Example 3-9. I'm also surprised that the author hasn't mentioned d'Alembert's principle (or virtual work for that matter) -- something that engineers make extensive use of -- anywhere in this book. > Since I'm not invoking the phrase "coordinate invariant" here I don't know what the deal is. You did mention that this book introduces mechanics in a coordinate-free manner (which this book actually doesn't). > It's nonconventional and may change your perspective if you really give it a chance. It's not just unconventional, this book is filled with terrible examples and techniques to solve problems and the author has reinvented the wheel in several places. The reason you found this book challenging was because this book chooses to do problems using the most contrived methods possible. In fact, this is a book to show why one needs analytical mechanics.
- ironmagma 7y ago
  > In fact, this is a book to show why one needs analytical mechanics I don't think the goal of the book is to obviate more advanced courses. It does well what it sets out to do, which is lay a foundation of dynamics. Contrasting it with other dynamics books I've read through, this one is self-consistent and much easier to follow the math on. Yes, the solutions are often long-winded, but that is the cost you pay for having a system. Other books like Introduction to Space Dynamics are very hand-wavey and not easy to check your work or find where you made a mistake, not to mention you must pick your coordinate systems very carefully and up front. Coordinate systems should not dictate the physics; it should be the other way around. Besides, this methodology is applicable to other circumstances beyond just dynamics. The rigorous approach to dealing with reference frames and coordinate systems is well applied to other fields like computer graphics, regardless of whether Lagrangian is more well suited to mechanical applications. > coordinate-free manner Yes, I said that, not coordinate invariant, and in fact my description was deliberately as devoid of jargon as I could make it. It should be taken as plain English. > It's not just unconventional, this book is filled with terrible examples and techniques to solve problems Considering Dr. Rao's successful tenure working at Draper as well as working on NASA spacecraft and other military vehicles, plus running a vehicle dynamics lab, I'm inclined to believe it has value beyond what you believe it to. Though I would be interested to read your textbook when it comes out, and I do appreciate the perspective.
  - b215826 7y ago
    > Other books like Introduction to Space Dynamics are very hand-wavey... Coordinate systems should not dictate the physics; it should be the other way around. It seems like you've not tried reading actual physics books written by real physicists and have only purveyed books known to a handful of engineering specialists, and have come to the conclusion that this is the best book for learning mechanics. I also fail to see why specialists wouldn't want to make use of methods that would make their lives easier and instead would want to dredge through pages of pointless algebra. > The rigorous approach to dealing with reference frames and coordinate systems is well applied to other fields like computer graphics In most universities around the world such things are taught as part of a standard vector calculus course or a mathematical methods course. You don't need this book (or any mechanics book for that matter) to learn such things. > Though I would be interested to read your textbook when it comes out I'll ignore the snideness of your comment, but will suggest that it's perhaps not a good idea to recommend/use books that take haphazard approaches for solving standard problems (some that were solve almost three centuries ago). In any case, my "textbook" would not look very different from the other 99% of textbooks written on analytical mechanics. If you want a recommendation, pick up Cornelius Lanczos's The Variational Principles of Mechanics [1], which is a real classic and a gem of a book. [1] https://www.amazon.com/Variational-Principles-Mechanics-Dover-Physics/dp/0486650677 https://www.amazon.com/Variational-Principles-Mechanics-Dove...

b215826 7y ago

> Considering you've spent all this time arguing that it's not straightforward (it is), I really suggest you take a look. I just downloaded a copy of the book from LibGen. I change my original assessment that it might be a good introductory book. In fact, now I think that this is a terrible book that reinvents the wheel in so many places, and novices should avoid it since it teaches bad practices. E.g., look at Example 3-2 of the book where the task is to find the motion of the particle constrained on a parabola y = r^2/2R (similar to the paraboloid example I asked, but more easier since the constraint manifold is one-dimensional). The solution of that problem (Eq. 3-105) is 4 pages of algebra! The Lagrangian for the system expressed in terms of r is L = m/2*(1 + r^2/R^2)*v^2 - (mg/2R)*r^2, v being dr/dt. Now, to find Eq. 3-105, which the author derives in 4 pages, all it takes is to plug this Lagrangian into the Euler-Lagrange equations, and answer pops out in 2-3 lines of algebra involving some very trivial partial derivatives. Curiously, the author has also reinvented d'Alembert's principle when he does this problem the second time in Example 3-9. I'm also surprised that the author hasn't mentioned d'Alembert's principle (or virtual work for that matter) -- something that engineers make extensive use of -- anywhere in this book. > Since I'm not invoking the phrase "coordinate invariant" here I don't know what the deal is. You did mention that this book introduces mechanics in a coordinate-free manner (which this book actually doesn't). > It's nonconventional and may change your perspective if you really give it a chance. It's not just unconventional, this book is filled with terrible examples and techniques to solve problems and the author has reinvented the wheel in several places. The reason you found this book challenging was because this book chooses to do problems using the most contrived methods possible. In fact, this is a book to show why one needs analytical mechanics.

ironmagma 7y ago
> In fact, this is a book to show why one needs analytical mechanics I don't think the goal of the book is to obviate more advanced courses. It does well what it sets out to do, which is lay a foundation of dynamics. Contrasting it with other dynamics books I've read through, this one is self-consistent and much easier to follow the math on. Yes, the solutions are often long-winded, but that is the cost you pay for having a system. Other books like Introduction to Space Dynamics are very hand-wavey and not easy to check your work or find where you made a mistake, not to mention you must pick your coordinate systems very carefully and up front. Coordinate systems should not dictate the physics; it should be the other way around. Besides, this methodology is applicable to other circumstances beyond just dynamics. The rigorous approach to dealing with reference frames and coordinate systems is well applied to other fields like computer graphics, regardless of whether Lagrangian is more well suited to mechanical applications. > coordinate-free manner Yes, I said that, not coordinate invariant, and in fact my description was deliberately as devoid of jargon as I could make it. It should be taken as plain English. > It's not just unconventional, this book is filled with terrible examples and techniques to solve problems Considering Dr. Rao's successful tenure working at Draper as well as working on NASA spacecraft and other military vehicles, plus running a vehicle dynamics lab, I'm inclined to believe it has value beyond what you believe it to. Though I would be interested to read your textbook when it comes out, and I do appreciate the perspective.
- b215826 7y ago
  > Other books like Introduction to Space Dynamics are very hand-wavey... Coordinate systems should not dictate the physics; it should be the other way around. It seems like you've not tried reading actual physics books written by real physicists and have only purveyed books known to a handful of engineering specialists, and have come to the conclusion that this is the best book for learning mechanics. I also fail to see why specialists wouldn't want to make use of methods that would make their lives easier and instead would want to dredge through pages of pointless algebra. > The rigorous approach to dealing with reference frames and coordinate systems is well applied to other fields like computer graphics In most universities around the world such things are taught as part of a standard vector calculus course or a mathematical methods course. You don't need this book (or any mechanics book for that matter) to learn such things. > Though I would be interested to read your textbook when it comes out I'll ignore the snideness of your comment, but will suggest that it's perhaps not a good idea to recommend/use books that take haphazard approaches for solving standard problems (some that were solve almost three centuries ago). In any case, my "textbook" would not look very different from the other 99% of textbooks written on analytical mechanics. If you want a recommendation, pick up Cornelius Lanczos's The Variational Principles of Mechanics [1], which is a real classic and a gem of a book. [1] https://www.amazon.com/Variational-Principles-Mechanics-Dover-Physics/dp/0486650677 https://www.amazon.com/Variational-Principles-Mechanics-Dove...