Finding torque from gyroscopic effect

[TomVu]

Hello everyone, I have a problem while calculate dynamic for gyroscope system on bicycle. I use Lagrange's equation for modelling precession effect, with generalized coordinate is a angular, the applied generalized force will be a torque. The model of gyroscope system like picture below:

I've found it in many papers but just got only one equation like this one and I still not understood it:

• torque of gyro = angular momentum of gyro * angular velocity of gimbal axis (1)

For calculate the torque, I just know the way like this:

That equation above seem not related with the equation I have found (1). If you have any idea for solve this problem, please tell me. I would be very appreciated for your help.

 

[eljose79]

Hello,

Thank you for sharing your problem with us. It seems like you are trying to calculate the dynamics of a gyroscope system on a bicycle and are using Lagrange's equations to model the precession effect. From your post, it seems like you have found an equation relating the torque of the gyroscope to its angular momentum and the angular velocity of the gimbal axis. However, you are not sure how this equation is related to the one you have found in your research.

Firstly, let's look at the equation you have found:

torque of gyro = angular momentum of gyro * angular velocity of gimbal axis (1)

This equation is known as the gyroscopic torque equation and it relates the torque of the gyroscope to its angular momentum and the angular velocity of the gimbal axis. This equation is derived from the conservation of angular momentum and is commonly used in the analysis of gyroscopic systems.

Now, let's look at the equation you have shared in your post:

This equation relates the torque of the gyroscope to the mass of the gyroscope, its distance from the pivot point, and its angular acceleration. This equation is derived from Newton's second law and is commonly used in the analysis of rigid body dynamics.

To understand how these two equations are related, we need to consider the dynamics of a gyroscope system. The gyroscopic torque equation (1) is used to model the precession effect, which is the tendency of the gyroscope to maintain its orientation in space. On the other hand, the equation you have shared in your post is used to model the overall dynamics of the gyroscope, taking into account its mass, distance from the pivot point, and angular acceleration.

To calculate the torque of the gyroscope, you can use either of these equations, depending on the specific situation and the information you have available. If you have the angular momentum and the angular velocity of the gimbal axis, you can use equation (1). If you have the mass, distance from the pivot point, and angular acceleration of the gyroscope, you can use the equation you have shared in your post.

I hope this explanation helps you understand the relationship between these two equations and how they can be used to calculate the dynamics of a gyroscope system on a bicycle. If you have any further questions, please do not hesitate to ask. Best of luck with your research!