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SeReNiTy
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Could someone point me in the correct direction from deriving Nielson's form from Lagranges equations?
That is where i got it from...arildno said:There is a nice exercise about that in Goldstein
The Nielson form of Lagrange's Equations is a set of equations that are used to describe the motion of a system in terms of its generalized coordinates and velocities. It is an alternative form of Lagrange's Equations that can be derived from the standard form using a transformation matrix.
The Nielson form is advantageous because it reduces the number of equations that need to be solved. In the standard form, there is one equation for each generalized coordinate, whereas in the Nielson form, there is only one equation for each degree of freedom.
To derive the Nielson form, you first need to determine the transformation matrix for your system. This matrix is then used to transform the standard form of Lagrange's Equations into the Nielson form. This process involves taking the partial derivatives of the transformation matrix with respect to the generalized coordinates and velocities.
The Nielson form is most commonly used when dealing with systems that have constraints, such as systems with fixed joints or rigid bodies. It is also useful for systems with a large number of degrees of freedom, as it simplifies the equations that need to be solved.
The Nielson form has many applications in physics and engineering. It is often used in the analysis of mechanical systems, such as robots and vehicles. It can also be applied to systems in thermodynamics, electromagnetics, and other fields where the motion of a system can be described by generalized coordinates and velocities.