Motion of pointed bodies - numerical methods

In summary, for solving the problem of finding trajectories of three pointed bodies in 2D, using Verlet's algorithm would be a good choice and polar coordinates may also be a useful alternative to cartesian coordinates.
  • #1
piotr_kow
3
0
Hi,
I have to solve (using numerical methods) fallowing problem: there are for example three pointed bodies in 2D. I have to find trajectories of their motions in their own gravitational field.
In cartesian coordinates for each body and direction I write equation of motion (that gives me system of 6 equations).

And my questions:
1) Which algorithm will be the best to solve this system of equations? (Will it be Verlet's algorithm?)?
2) Maybe there are some coordinates which are better then cartesian in this problem?

greetings :)
 
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  • #2
1) Yes, Verlet's algorithm is a great option for solving this system of equations. It is an efficient and accurate numerical method for integrating Newton's equations of motion. 2) You can also use polar coordinates in this problem, as they can be useful in describing the motion of multiple bodies in two dimensions. This is because polar coordinates can provide an easier way to calculate distances between the bodies, as well as angles associated with the gravitational field of each body.
 

1. What are numerical methods for motion of pointed bodies?

Numerical methods are mathematical techniques used to solve problems involving motion of pointed bodies. These methods involve breaking down the complex equations governing the motion into smaller, simpler equations that can be solved using numerical calculations. This allows for more accurate and efficient solutions compared to traditional analytical methods.

2. How do numerical methods differ from analytical methods in studying motion of pointed bodies?

Numerical methods use numerical calculations to approximate the solution to a problem, while analytical methods use exact mathematical equations to solve problems. In studying motion of pointed bodies, numerical methods are typically used for more complex and non-linear systems, while analytical methods are better suited for simpler and linear systems.

3. What are the advantages of using numerical methods for studying motion of pointed bodies?

Numerical methods offer several advantages, including the ability to handle complex systems, the ability to incorporate real-world factors such as friction and air resistance, and the ability to handle non-linear systems. They also allow for more accurate solutions compared to analytical methods, especially for systems with multiple variables.

4. What are some common numerical methods used for studying motion of pointed bodies?

Some common numerical methods used for studying motion of pointed bodies include Euler's method, Runge-Kutta methods, and the Verlet algorithm. These methods vary in their complexity and accuracy, and are often chosen based on the specific problem being studied.

5. How do scientists validate the results obtained from numerical methods for motion of pointed bodies?

Scientists use a variety of methods to validate the results obtained from numerical methods, such as comparing the results to analytical solutions, conducting experiments to verify the results, and performing sensitivity analyses to test the robustness of the solutions. They also continually refine and improve the numerical methods to increase their accuracy and applicability.

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