Equations of motion for 4 dof

In summary, to find the angular speeds for roll-pitch-yaw angles, you can use rotational kinematics equations, and to obtain v and w in the body frames, you can use transformation matrices for rotation.
  • #1
steinc
1
0
Hi all,
I'm working on a project to control the angles of a beam(purple) with a quadcopter(orange),see figure below. The angles for both the ground-beam and beam-quadcopter will be measured with joysticks, so only roll and pitch angles will be measured and the yaw rotation is fixed.
To obtain the equation of motion of this system I started with the method of Lagrange:
L = T-V.
With T the kinetic energy: ½mvTv + ½wTIw
and V the potential energy: mgz
and this for both the beam and the quadcopter.
I started with the roll-pitch-yaw rotation matrices (so rotation around the fixed axes) but I do not know how to get the angular speed out of them.
So my first question is how to find the angular speeds for roll-pitch-yaw angles and my second question is how to obtain the v and the the w in de body frames (that's the easiest for the moment of inertia I think)?Thanks
upload_2016-2-28_17-35-9.png
 
Engineering news on Phys.org
  • #2
for your help!Hello,

Thank you for sharing your project with us. It sounds like an interesting and challenging project. To answer your first question, the angular speeds for roll, pitch, and yaw can be found using the rotational kinematics equations. These equations relate angular velocity (w) to angular displacement (theta) and time (t). The equations are as follows:

w = theta/t

Where w is the angular speed, theta is the angular displacement, and t is the time interval.

For your second question, to obtain v and w in the body frames, you will need to use the transformation matrices for rotation. These matrices will allow you to transform the velocities and angular velocities from one frame to another. For example, if you have the velocities and angular velocities in the ground frame, you can use the rotation matrices to transform them into the body frame.

I hope this helps and good luck with your project! Let us know if you have any further questions.
 

What are "Equations of motion for 4 dof"?

The equations of motion for 4 dof refers to a set of mathematical equations that describe the motion of a system with four degrees of freedom (dof). These equations are used in mechanics and physics to model the motion of objects and systems with multiple moving parts.

What are degrees of freedom (dof) in the context of equations of motion?

Degrees of freedom (dof) refer to the number of independent variables or parameters that are needed to fully describe the motion of a system. In the context of equations of motion, a system with 4 dof means that four independent variables are required to describe its motion.

What is the significance of equations of motion for 4 dof in science?

Equations of motion for 4 dof are an important tool in science as they allow us to mathematically model and predict the behavior of systems with multiple moving parts. These equations are used in fields such as mechanics, physics, and engineering to understand and analyze the motion of various objects and systems.

What are some common applications of equations of motion for 4 dof?

Equations of motion for 4 dof have many practical applications, such as in designing and analyzing mechanical systems, predicting the motion of celestial bodies, and understanding the behavior of molecules and atoms. They are also used in fields like robotics and computer animation to simulate the movement of objects.

Are there any limitations or assumptions associated with equations of motion for 4 dof?

Like any mathematical model, equations of motion for 4 dof have limitations and make certain assumptions. For example, they may not accurately describe systems with complex or non-linear motion. They also assume that the forces acting on the system are known and can be accurately measured.

Similar threads

  • Mechanical Engineering
Replies
3
Views
326
  • Introductory Physics Homework Help
Replies
7
Views
982
  • Mechanical Engineering
Replies
5
Views
1K
Replies
1
Views
1K
  • General Engineering
Replies
6
Views
3K
  • Mechanical Engineering
Replies
8
Views
3K
Replies
2
Views
797
  • Introductory Physics Homework Help
Replies
4
Views
662
Replies
14
Views
1K
Replies
10
Views
2K
Back
Top