What You Will Learn!
- Writting Lagrangian (Lagrange function) of a mechanical system in a generalized coordinate system, and transforming it to a function of independent coordinates.
- Writting Euler-Lagrange equations (Lagrange's equations of second kind) using Lagrange function of independent coordinates, and finding equations of motion.
- Writting Lagrange's equations of first kind using Lagrange function of both dependent and independent coordinates, and finding forces of constraint.
- Finding conserved generalized momentums (corresponing to the cyclic coordinates), and conserved energy (if Lagrangian is not a implicit function of time).
Description
This is an introductory course in Lagrangian mechanics provided for college students and anyone who is familiar with Newtonian mechanics and calculus.
In this course you will learn how to apply Lagrangian mechanics to the classical systems and find their equations of motion and physical quantities. When applied to the classical systems, Lagrangian mechanics is equivalent to the Newtonian mechanics, but more easier than it, especially when you are dealing with more complicated systems.
This course is made of three sections:
section 1: this section begins with writing Lagrangian (Lagrange function) of a system in a generalized coordinates in terms of independent coordinates, by finding constraint functions and number of degrees of freedom of the system. You will learn how to apply Euler-Lagrange equations (Lagrange's equations of the second kind) to the independent coordinates and find the equations of motion of the system. Lagrangian of classical systems is discussed along with three examples.
Section 2: This section begins with definition of generalized conservative forces. Then by writing Lagrangian without imposing constraint functions and by applying Euler-Lagrange equations of first kind, you learn how to find constraint forces of a system.
Section 3: in this section you learn how to find conserved generalized momentum (both linear and angular) if there is a cyclic coordinate in Lagrangian; and how to find conserved energy of the system if Lagrangian is independent of time.
Register to this course and enjoy learning Lagrangian mechanics!
Who Should Attend!
- Undergraduate Students
- Anyone who wants to learn Lagrangian Mechanics.
