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Where did you get the idea that there is no such thing as direction in space? I assume you're confusing the microgravity in a spacecraft with "no direction". Indeed, in a completely enclosed spacecraft, without windows, you cannot tell which way the earth (or the moon, the sun, etc) are. However, they are still very much in a particular direction, even if ...

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But when in space, there is no such thing called direction. In space, you have to first choose a frame of reference in order to measure or calculate vector quantities. The choice is arbitrary but whatever choice you make, you will end up with the same answer. Some choices make the calculations easier. For example, you could identify a nearby small ...

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Schaum series Differential Geometry will solve part of your problem. Search "problem book in riemannian geometry" on google and it should bring out something useful. Also see V.I. Arnold's books.

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As you described the book you are searching for I thought of a book that fit that description except it may not be the same book. I have a text book for a course given at Cal Berkeley by Professor Richard A. Muller. It is called "Physics and Technology for Future Presidents" with a subtitle of "An Introduction to the Essential Physics Every World Leader ...

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The problem is that many "human scale" phenomena are terribly difficult to treat: friction, fluid dynamics, vorticity, heat transfer... Even if they are ubiquitous in our everyday lives, these things are really difficult (and sometimes impossible!) to treat analytically. Just think about friction: the microscopic mechanisms behind this force that rules our ...

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You should study Newtonian mechanics before Lagrangian mechanics because Newtonian mechanics is more general than Lagrangian mechanics. In other words, while whenever a system allows a Lagrangian formulation it also allows a Newtonian formulation, the converse is not true; the quintessential case is dynamics in the presence of dissipative forces. Lagrangian ...

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No, I would highly recommend studying Newtonian mechanics before Lagrangian mechanics. While, yes it is 'possible' to learn about Lagrangian mechanics before Newtonian, a lot of intuition would be lost beginning with one instead of the other which will, in the long run, do no more than harm you or, at best, possibly confuse you. But there are, indeed, many ...

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It is necessary to study Newtonian mechanics to truly understand Lagrangian mechanics since its underlying foundation is Newtonian mechanics. It is essentially a different formulation of the same thing. In a way when doing Lagrangian mechanics you are still doing Newtonian mechanics just in the way of energy. For example, under Lagrangian mechanics, say we ...

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In almost every technical field, one of the key goals of an undergraduate degree is to prepare one to work as a professional in that field. Working as a professional physicist pretty much means having a PhD in physics. The key focus of an undergraduate physics degree is to prepare students to enter a graduate school program in physics. Excluding ...

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Most of the "intermediate scale" problems were "solved" long ago, and are now mostly the domain of engineering: application of physics to real world problems. I put "solved" in quotes: "real world" solutions require that you don't make all the simplifying assumptions that make many problems "solvable" - this is no such thing as a spherical cow. Nonlinearity, ...

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"What Einstein was really looking for was a new way to transform between reference frames that would keep the laws of electrodynamics invariant inasmuch as the Galilean transformations keep the laws of Newton invariant?" It wasn't so much about finding the transformations, because the Lorentz transformations had been known for a while at the time, since ...

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$I$ has a clear physical meaning if $I\lt 0$ – which is a significant percentage of the spacetime, so to say: $$I = -c^2\Delta t_{\rm proper}^2$$ where $\Delta t_{\rm proper}$ is the time measured by clock that moves by a constant velocity (without acceleration); and that visits the point $(x_1,y_1,z_1)$ at time $t_1$ and $(x_2,y_2,z_2)$ at time $t_2$. ...

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