- #1
least_action
- 22
- 0
Is it possible to do statics using lagrangians? (specifically building up a compound shape like a bridge from constrained point masses). Where could I see an example of this?
least_action said:Is it possible to do statics using lagrangians? (specifically building up a compound shape like a bridge from constrained point masses). Where could I see an example of this?
fobos3 said:Yes, just put the Lagrangian equal to the potential energy. However I think you will find that, if you have an equilibrium the potential energy is at minimum more useful. For example consider the cantenary.
[tex]V=\int_C my\,ds[/tex]
Now if you use Lagrangian mechanics you would be minimising [tex]\iint_C my\,ds\,dt[/tex] instead of [tex]\int_C my\,ds[/tex]
A Lagrangian is a mathematical function that describes the dynamics of a physical system in terms of its position, velocity, and time. It is commonly used in classical mechanics to analyze the motion of objects.
A Newtonian approach uses the concept of forces to explain the motion of objects, while a Lagrangian approach uses the concept of energy. This means that Lagrangians can be used to analyze systems with complex geometry and constraints, whereas Newtonian methods may not be applicable.
Yes, Lagrangians can be used for both dynamics and statics. In statics, Lagrangians are used to find the equilibrium configuration of a system, where the net force and torque are equal to zero.
A compound shape is a complex shape that is made up of simpler shapes, such as rectangles, triangles, or circles. In the context of Lagrangians for statics, compound shapes are used to represent real-world objects or systems that have irregular or non-uniform geometries.
One example is using Lagrangians to analyze the equilibrium of a bridge. The bridge can be represented as a compound shape made up of multiple rectangular and triangular sections. By using Lagrangians, we can find the forces and torques acting on each section and determine if the bridge is in a stable or unstable equilibrium.