Sum of infinitesimal rotations around different points in 2D space ?

In summary, the sum of infinitesimal rotations around different points in 2D space results in a net rotation around a single point. This concept, known as rotational motion, is used to describe the movement of objects in two-dimensional space and is essential in understanding rotational dynamics and kinematics. The sum of infinitesimal rotations can also be used to calculate the angular velocity and acceleration of an object, providing valuable insights into its motion. Overall, understanding the sum of infinitesimal rotations is crucial in analyzing and predicting the behavior of objects in 2D space.
  • #1
pL1
7
0
Hello,

in order to numerically solve a physics problem I think I need to add 2 (infinitesimal) rotations of one and the same segment each around a different point in 2D space in one iteration of numeric approximization. How does this addition work out? Is it the sum of the vectors connecting the startpoint of each rotation with its endpoint? I don't find a conclusive solution.

Thanks!

Details here: https://www.physicsforums.com/showthread.php?t=333476"
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Should be ##R_2(R_1(s)+v_{12})-v_{12}## with a segment point ##s##, ordinary rotations ##R_i## and the translation vector ##v_{12}## between the two centers of rotation.
 

1. What is an infinitesimal rotation?

An infinitesimal rotation is a small, imperceptible rotation that occurs around a point in 2D space. It is often described as a change in orientation or direction, but on a very small scale.

2. How is the sum of infinitesimal rotations calculated?

The sum of infinitesimal rotations is calculated by adding together the individual rotations around different points in 2D space. This is usually done by using vector algebra or matrix multiplication.

3. What is the significance of considering infinitesimal rotations?

Infinitesimal rotations are important in mathematical and scientific contexts because they allow for the analysis of continuous, smooth movements. They are also used in physics, engineering, and computer graphics to model and simulate motion.

4. Can infinitesimal rotations be applied to 3D space?

Yes, infinitesimal rotations can be applied to 3D space as well. However, the calculations and equations become more complex as they involve three dimensions instead of two.

5. What are some real-life applications of infinitesimal rotations in 2D space?

Infinitesimal rotations in 2D space have many practical applications, such as in robotics, computer animation, and video game development. They are also used in navigation systems, such as GPS, to accurately track and predict the movement of objects.

Similar threads

A Proper Multi-Axis Rotational Analysis Method
    • Classical Physics
Replies
7
Views
790
I Exploring Special Relativity: Patterns, Conjectures and Questions
    • Special and General Relativity
Replies
3
Views
1K
Rotations of 3-Spheres: Exploring 4D Space & Beyond
    • Linear and Abstract Algebra
Replies
13
Views
2K
B Swimming pool in a rotating space station
    • Classical Physics
Replies
26
Views
2K
Spin-1 particle states as seen by different observers: Wigner rotation
    • Advanced Physics Homework Help
Replies
5
Views
2K
B Invariant under rotation: Banal, obvious, or noteworthy?
    • General Math
Replies
2
Views
1K
I Effective Hamiltonian to Rotational Term Values
    • Atomic and Condensed Matter
Replies
0
Views
371
I Find an explicit formula for this n-sum problem
    • General Math
Replies
7
Views
1K
I Different norms and how L1 leads to the sparsest solution
    • General Math
Replies
1
Views
749
Understanding Curl in 2D/3D Space
    • Other Physics Topics
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top