Classical Dynamics of Particles & Systems

In summary, the conversation discusses deriving equations for the rotation of a coordinate system in Classical Dynamics of Particles & Systems, chapter 1. The main question is about the projection of x2 on the x'1 and the equality of two vectors. The person also asks about resizing an image and the use of an asterisk in the problem statement. The conversation also references reading the errata for the book and a better diagram for understanding the concepts.
  • #1
Dr_Pill
41
0
This is an image of Classical Dynamics of Particles & Systems, chapter 1

In deriving the equations for the rotation of a coordinate system

wuNFqPU.jpg


I understand the equations 1.2a & 1.2b b, but why is the projection of x2 on the x'1 equal to ab +bc

and why is the vector de equal to the vector Of?

I tried the whole afternoon drawing triangles, writing vectors as one another, cosinus,sinus rules, congruent triangles everything I could think off, yet I can't prove it.
It seems obvious, but I want proof :D

(how to resize my image)

(btw, this is self-study, no homework or anything like that)
 
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  • #2
What does the asterisk in the problem statement indicate?
 
  • #3
I don't know the answers to your questions. It's worth reading the errata for the book, even if it isn't relevant to this particular problem: http://astro.physics.sc.edu/Goldstein/
 
  • #4
Stephen Tashi said:
I don't know the answers to your questions. It's worth reading the errata for the book, even if it isn't relevant to this particular problem: http://astro.physics.sc.edu/Goldstein/

It's not Goldstein. But from Marion Jerry, but ok, will check errata.

sapratz said:
What does the asterisk in the problem statement indicate?

Just saying that x1,x2,x3 are equivalent to x,y,z in the Cartesian plane.
 

1. What is classical dynamics?

Classical dynamics is a branch of physics that studies the motion of particles and systems under the influence of forces. It is based on Newton's laws of motion and the principles of conservation of energy and momentum.

2. What is the difference between classical and quantum dynamics?

Classical dynamics deals with macroscopic objects and their motion, while quantum dynamics deals with microscopic particles and their behavior. Classical dynamics is deterministic, meaning that the future state of a system can be predicted with certainty, while quantum dynamics is probabilistic, meaning that the future state can only be described in terms of probabilities.

3. What are some common applications of classical dynamics?

Classical dynamics has many practical applications, including understanding the motion of planets and other celestial bodies, designing and analyzing mechanical systems such as engines and structures, and predicting the trajectories of projectiles in fields such as ballistics.

4. How is classical dynamics related to other branches of physics?

Classical dynamics is closely related to other branches of physics, such as classical mechanics, thermodynamics, and electromagnetism. It provides the foundation for these fields and is often used in conjunction with them to solve problems and make predictions about the behavior of physical systems.

5. What are some key principles in classical dynamics?

Some key principles in classical dynamics include Newton's three laws of motion, the principle of conservation of energy, and the principle of conservation of momentum. These principles serve as the fundamental building blocks for understanding and analyzing the motion of particles and systems in classical physics.

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