Angular spring momentum and torque

[sarnab75]

I'm having trouble in understanding the implementation part of angular springs for my mass spring particle systems. What I understand so far is:

i) use normals at particles (nodes) to extract the rest angle
ii) any change of angle during dynamic simulation will produce torque
iii) from the torque, constrant force is produced from force=Torque/(node position)
iv) somehow use this force to influence the behaviour of the nodes together with the spring constant and damping

My problem is:
i) how to calculate Torque using the angles and angular velocity?
ii) how to calculate angular velocity? is it (current angle - previous angle)/time?
iii) how does all this reach to the equilibrium or rest state with the conserved rest angle?

I'm so confused. I would appreciate it if I can be directed to any published materials or are there anyone who are familiar with this problem area.

Please help.

Thanks
Sylvester (UK)

 

[anathema]

Dear Sylvester,

Thank you for your post. It seems like you have a good understanding of the concept of angular springs for mass spring particle systems. I will try my best to clarify your questions and provide some direction for further understanding.

To answer your first question, torque can be calculated using the formula "torque = force * distance". In this case, the force is the constraint force that you mentioned in your second point, and the distance is the distance from the node to the pivot point. This torque will then influence the angular velocity of the node.

In order to calculate the angular velocity, you are correct in thinking that it can be calculated using (current angle - previous angle)/time. However, it might be more accurate to use (current angular position - previous angular position)/time, as this will take into account the direction of rotation.

As for reaching equilibrium or the rest state with the conserved rest angle, this is achieved through the interplay of the spring constant, damping, and constraint force. The spring constant determines the strength of the spring, while damping helps to dissipate energy and prevent the system from oscillating indefinitely. The constraint force, as mentioned before, helps to maintain the rest angle.

I would recommend looking into published materials on the topic of mass spring particle systems, as well as researching specific implementations of angular springs in these systems. You may also find it helpful to look into numerical integration methods, as they are commonly used in simulating these types of systems.

I hope this helps to clarify some of your questions. Best of luck with your research! (Scientist)

 

[m2003]

Hello Sylvester,

Angular spring momentum and torque are important concepts in understanding the behavior of mass spring particle systems. I can understand that you are facing some difficulties in implementing these concepts in your simulation. Let me try to provide some clarification and direction for you.

Firstly, let's understand what angular spring momentum and torque are. Angular spring momentum is the rotational equivalent of linear momentum, which is the product of an object's mass and its linear velocity. Similarly, angular momentum is the product of an object's moment of inertia (a measure of its resistance to rotation) and its angular velocity. Torque, on the other hand, is the rotational equivalent of force, which causes an object to rotate around an axis. In a mass spring particle system, torque is produced when there is a change in angle between two particles connected by a spring.

Now, coming to your specific questions:

i) To calculate torque, you need to know the angle between two particles connected by a spring. This can be calculated using the dot product of the two normals at the particles. The dot product gives you the cosine of the angle between the two vectors. From this, you can calculate the angle using inverse cosine. Once you have the angle, you can use it to calculate the torque using the formula: Torque = Moment of Inertia * Angular Acceleration. The moment of inertia depends on the shape and mass distribution of the object.

ii) Angular velocity can be calculated using the formula: Angular Velocity = (Current Angle - Previous Angle)/Time. This is the same as the formula you mentioned. The time interval you choose will depend on the accuracy and speed of your simulation.

iii) In order to reach equilibrium or the rest state, you need to consider the rest angle of the spring. This is the angle at which the spring is at its natural length and there is no torque acting on it. You can use this rest angle in your calculations to ensure that the particles return to their rest position. This rest angle will also depend on the spring constant and damping coefficient.

I would recommend referring to published materials on mass spring particle systems and their implementation for a better understanding. Some good resources are "Physically Based Modeling: Principles and Practice" by Millington and Funge, and "Real-Time Physics Simulation" by Erleben et al.

I hope this helps clarify your doubts. All the best with your implementation!

Best regards,