Calculating angle from body-fixed moments on a ridig body

In summary: Your Name]In summary, the forum member is seeking help with calculating the rigid body angle based on its local moment in R3 space. They mention using the rotational acceleration as a function of distance and the directional cosine matrix to update the rotation matrix. They also consider numerically integrating the local angular acceleration and using the constraint equation to calculate the angle. They are seeking clarification on the best approach and may consult with other experts for their insights.
  • #1
Larsen1000
2
0
Hello everyone

I have some problems figuring out the correct way to calculate my rigid body angle based its local moment. I am working in R3 space.

I have the rigid body local rotational acceleration expressed as a function of distance to fulfill a rigid body constraint:

AlphaL = F(x,z) * l(x,z) I

I want to find a way to updating my rotation matrix in each iteration expressed by the equation for rotational acceleration equation.

My first thought was to numerically integrate the local angular acceleration to get the local angular velocity. To get the angles I am using the the directional cosine matrix to update the rotation matrix.

Am I thinking correctly?
 
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  • #2




Thank you for reaching out for help with your problem. I can offer some suggestions on how to approach this issue.

Firstly, it is important to clarify what exactly you are trying to calculate. Are you looking for the rigid body angle at a specific point in time, or are you trying to track the changes in the angle over time? This will help determine the appropriate method to use.

In general, one way to calculate the rigid body angle is by using the Euler angles or the quaternion representation. These methods involve rotating the rigid body around three axes or using a four-dimensional vector, respectively. However, if you are working in R3 space and have a constraint equation, it might be more appropriate to use a different approach.

You mentioned numerically integrating the local angular acceleration to get the local angular velocity. This can be a valid approach, but it is important to ensure that your integration method is accurate and stable. You may also need to consider the effects of numerical errors and how they can impact your results.

Another approach could be to use the constraint equation to directly calculate the rigid body angle. This method would involve solving for the angle using the constraint equation and possibly using a numerical solver to obtain a solution.

Overall, it is important to carefully consider your problem and the available methods before deciding on an approach. It may also be helpful to consult with other scientists or experts in the field for their insights and suggestions.

Best of luck with your calculations.
 

1. How do you calculate the angle from body-fixed moments on a rigid body?

To calculate the angle from body-fixed moments on a rigid body, you need to use the formula: angle = moment / (inertia * angular velocity). This formula takes into account the moment acting on the body, the inertia of the body, and the angular velocity of the body.

2. What is the significance of calculating the angle from body-fixed moments?

The angle calculated from body-fixed moments helps in understanding the orientation and rotational motion of a rigid body. It is a crucial aspect in the study of mechanics and dynamics of objects.

3. Can the angle be negative when calculating from body-fixed moments?

Yes, the angle can be negative when calculating from body-fixed moments. This indicates a clockwise rotation of the body, while a positive angle indicates a counterclockwise rotation.

4. What is the difference between body-fixed moments and external moments?

Body-fixed moments are moments that act on a rigid body due to its own inertia, while external moments are moments that act on the body from external forces. Calculating the angle from body-fixed moments only takes into account the former, while external moments must be considered separately.

5. Are there any limitations to calculating the angle from body-fixed moments?

Yes, there are limitations to calculating the angle from body-fixed moments. This method assumes that the body is rigid and has a constant moment of inertia. It also does not take into account any external forces acting on the body, which can affect its motion. Real-life objects may not always behave as perfectly rigid bodies, so these limitations should be considered when using this formula.

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