Hamiltonian mechanics. I roughly understand the idea behind the Hamiltonian of a system, but I'm utterly confused as to what the hell a Hamiltonian vector field is. I've taken ODE's, PDE's, Linear Algebra, and I'm just being introduced to Differential Geometry so I can handle the math, but every article I read on this subject is entirely too abstract or jargon filled for me to understand. Can someone please explain to me what this vector field is and what it represents?
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#2
Mar13-11, 06:35 AM
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Sci Advisor
P: 1,939
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#3
Mar13-11, 08:39 AM
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P: 306
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When we're doing Hamiltonian mechanics we're in phase space and so have local coordinates
So, just like any ordinary vector field you've seen before, if you're at point 'm' it tells you where to go next to follow along the vector field. Differential equations are vector fields. What's your background in mechanics? | |
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#4
Mar15-11, 11:23 PM
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P: 99
| Hamiltonian vector field
Haven't taken any mechanics courses. I mainly don't understand what a hamiltonian vector field physically represents. Would the components be the velocities and forces of a particle or what? If someone could just give me an example it would go a long way. Thanks
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#5
Mar16-11, 05:51 AM
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Sci Advisor
P: 1,939
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