Classical mechanics is the branch of physics concerned with describing the motion of bodies. The subject is based on three simple axioms relating forces and movement. These axioms were first postulated by Newton in the 17th century and are known as his three laws of motion. Lagrangian mechanics is a restatement of the Newtonian formulation. It deals with energy quantities and paths-of-motion instead of forces. This often makes it simpler to use when working with non-trivial mechanical systems. In this thesis, we use the Lagrangian method to model two such systems; A rotating torus and a variant of the classical double pendulum. It soon becomes clear that the complexity of these systems make them difficult to attack by hand. For this reason, we take a computer-based approach. We use a software-package called Sophia which is a plug-in to the computer algebra system Maple. Sofia was developed at the Department of Mechanics at KTH for the specific purpose of modeling mechanical problems using Lagrange’s method. We demonstrate that this method can be successfully applied to the analysis of motion of complex mechanical systems. The complete equations of motion are derived in a symbolic form and then integrated numerically. The motion of the system is finally visualized by means of 3D graphics software Blender.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-232119 |
| Date | January 2016 |
| Creators | Strand, Filip, Arnoldsson, Jakob |
| Publisher | KTH, Mekanik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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