Lagrange equation of motion for tensegrity

In summary, The conversation discusses two papers related to a 3-bar tensegrity based mobile robot and its dynamics. The first paper provides an equation of motion using the Euler-Lagrange method, but the individual's velocity and acceleration are unknown. The paper suggests using Runge-Kutta integration, but the individual struggles to understand how to define and proceed with this method. They also mention difficulty understanding how the tensegrity's positions are updated for movement.
  • #1
GeorgeL
1
0
Hi,
I have read this paper “Dynamic equations of motion for a 3-bar tensegrity based mobile robot” (1) and this one “Dynamic Simulation of Six-strut Tensegrity Robot Rolling”.

1) http://digital.csic.es/bitstream/10261/30336/1/Dynamic equations.pdf

I am trying to implement a tensegrity, actuated system following the first paper, but I came at a point that I calculate the Kinetic Energy, Potential Energy and virtual work of the system. I have to update the pose of each bar.

The paper gives me the equation of motion (Euler-Lagrange) but uses the velocity and acceleration that i don’t know how to calculate. It says at the end about using Runge-Kutta integration but I don’t understand how I will define them in the first place or how i will proceed. I cannot understand how it’s updating the positions for the tensegrity to move.

Thank you
 
Mathematics news on Phys.org

Related to Lagrange equation of motion for tensegrity

What is the Lagrange equation of motion for tensegrity?

The Lagrange equation of motion for tensegrity is a mathematical equation used to model the motion of a tensegrity structure. It is based on the principle of virtual work, where the total virtual work done by all forces acting on the structure is equal to zero. This equation takes into account the tension and compression forces in the structure and can be used to predict its behavior under different loading conditions.

How is the Lagrange equation of motion derived for tensegrity?

The Lagrange equation of motion for tensegrity is derived by using the principle of virtual work and the Lagrange multiplier method. This involves setting up a system of equations that describe the equilibrium of forces in the structure and then taking the derivative of the total virtual work with respect to the generalized coordinates. The resulting equations can then be solved to determine the motion of the structure.

What are the advantages of using the Lagrange equation of motion for tensegrity?

The Lagrange equation of motion for tensegrity offers several advantages over other methods of analyzing tensegrity structures. It takes into account both tension and compression forces, which are essential for accurately predicting the behavior of these structures. It also allows for the analysis of complex, multi-body systems and can be used to determine the optimal design of a tensegrity structure.

Are there any limitations to the Lagrange equation of motion for tensegrity?

While the Lagrange equation of motion is a powerful tool for analyzing tensegrity structures, it does have its limitations. It assumes that the structure is in static equilibrium and does not consider any dynamic effects, such as vibrations or impacts. Additionally, it may be difficult to apply to highly nonlinear structures or structures with large numbers of degrees of freedom.

How is the Lagrange equation of motion used in practical applications of tensegrity?

The Lagrange equation of motion is used in various practical applications of tensegrity, such as in the design and analysis of tensegrity robots, deployable structures, and space exploration systems. It is also used in biomechanics to model the movement of living organisms, as well as in architecture and art to create unique and innovative structures. Its versatility and accuracy make it a valuable tool in a wide range of fields.

Similar threads

I How to find the equation of motion using Lagrange's equation?
    • Classical Physics
Replies
13
Views
1K
A Lagrangian to the Euler-Lagrange equation
    • Classical Physics
Replies
1
Views
1K
I Exploring the Flexibility of Coordinates in Euler-Lagrange Equations
    • Mechanics
Replies
5
Views
898
I Action in Lagrangian Mechanics
    • Classical Physics
Replies
5
Views
1K
Lagrange Equations of Motion for a particle in a vessel
    • Mechanics
Replies
2
Views
1K
I Lagrangian approach for the inclined plane
    • Classical Physics
Replies
21
Views
2K
Derive the equations of motion
    • Advanced Physics Homework Help
Replies
4
Views
2K
Understanding Kinetic Energy: Moment of Inertia and Rotational Motion
    • Advanced Physics Homework Help
Replies
5
Views
931
I Simulating a 2-Phase Water System: Tips and Resources for Dynamic Simulation
    • Thermodynamics
Replies
4
Views
554
MHB Equations for Lagrange-Laguerre mesh
    • General Math
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top