# Simulating the Spiralling Motion of a Coin on a Table

• sreenathb
In summary, the conversation revolves around simulating the spiralling motion of a coin on a table. The person is having difficulties solving the problem and is looking for numerical methods to solve the three non-linear equations they have. Suggestions include using numerical integration techniques like Runge-Kutta or Euler, as well as gradient-based optimization algorithms such as Levenberg-Marquardt or Newton's Method.
sreenathb
i am trying to simulate the spiralling motion of a coin that is rolled on a table.i am having three equations...
1. the gyroscopic moment equation.
2. the conservation of energy equation.
3. general kinematic equation.

three unknowns...curvature radius,precession velocity and coin inclination.
the equations i am getting are non-linear.can someine suggest me any numerical methods to solve these approximately.
i want those which can be easily programmed.i tried one which uses the jacobian..bit found that the solution was not converging.

It sounds like you're trying to solve a difficult problem! Have you tried using numerical integration techniques, such as the Runge-Kutta method? This method is relatively easy to program, and can be used for non-linear equations. You could also look into the Euler method, which is a simpler numerical integration technique. Another option is to try a gradient-based optimization algorithm, such as Levenberg-Marquardt or Newton's Method. These may be able to help you find an approximate solution to your equations. Good luck!

I would suggest using numerical methods such as the Euler method or the Runge-Kutta method to solve these equations. These methods are commonly used in physics and can be easily programmed. You can also try using a software program such as MATLAB or Mathematica to solve the equations numerically. Additionally, it may be helpful to simplify the equations by making assumptions or approximations, as this can often make them easier to solve. Once you have a numerical solution, you can compare it to experimental data or analytical solutions to validate your results. It is also important to carefully check your equations and initial conditions to ensure they are correct and accurately represent the system you are trying to simulate.

## 1. How does the angle of the initial throw affect the spiralling motion of a coin on a table?

The angle of the initial throw determines the trajectory of the coin and can greatly affect the spiralling motion. If the coin is thrown at a high angle, the spiralling motion will be more pronounced and the coin will travel a shorter distance before falling. On the other hand, if the coin is thrown at a low angle, the spiralling motion will be less noticeable and the coin may travel a longer distance before falling.

## 2. What factors contribute to the duration of the spiralling motion of a coin on a table?

The duration of the spiralling motion of a coin on a table is affected by several factors, including the initial velocity and angle of the throw, the friction between the coin and the table surface, and the shape and weight distribution of the coin. A heavier and more symmetrical coin will typically have a longer spiralling motion compared to a lighter and more asymmetrical coin.

## 3. Is there a mathematical formula to accurately predict the trajectory of a coin's spiralling motion on a table?

While there are mathematical formulas that can be used to model the trajectory of a coin's motion, accurately predicting the exact path of a spiralling coin is challenging due to the complex interactions between the coin and the table surface. Factors such as air resistance and slight variations in the throw can also affect the trajectory. Therefore, it is more accurate to simulate the motion using computer software rather than relying solely on mathematical formulas.

## 4. How does the surface of the table affect the spiralling motion of a coin?

The surface of the table can have a significant impact on the spiralling motion of a coin. A rough or uneven surface can cause the coin to bounce or deviate from its intended path, while a smooth surface allows for a more consistent and predictable motion. Additionally, the coefficient of friction between the coin and the table surface can also affect the duration and speed of the spiralling motion.

## 5. Can the spiralling motion of a coin on a table be used to determine its properties?

The spiralling motion of a coin on a table can provide some insights into its properties, such as its weight distribution and shape. However, other factors such as air resistance and variations in the throw can also impact the motion, making it difficult to accurately determine the coin's properties based on its spiralling motion alone. Additional experiments and measurements may be needed for a more precise analysis.

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