PX285 - 0 - hamiltonian mechanics & fluid dynamics
*image: stallfish *
hamiltonian mechanics
A - introduction
PX285 - A1 - newton's laws
PX285 - A2a - conservation laws
PX285 - A2b - angular momentum
B - variational principles
PX285 - B1 - variational principles
PX285 - B2 - fermat's law in optics
PX285 - B3 - newtonian mechanics - the principle of least action
C - calculus of variations
PX285 - C1 - the euler-lagrange equation
PX285 - C2 - coordinate change
PX285 - C3 - newton's second law
PX285 - C4 - simple pendulum
PX285 - C5 - a roller-coaster
PX285 - C6a - multi-coordinate problems
PX285 - C6b - a particle in a cartesian plane
PX285 - C6c - two particles in 1D
PX285 - C6d - two particles in 3D
D - the hamiltonian
PX285 - D1 - the hamiltonian
PX285 - D2 - a constant of the motion
PX285 - D3 - the conservation of energy
PX285 - D4 - roller-coaster revisited
E - conservation laws and symmetries
PX285 - E1 - noether's theorem
PX285 - E2 - translation of space
PX285 - E3 - translation in time
PX285 - E4 - rotation of space
F - hamilton's equations
PX285 - F1 - hamilton's equations
PX285 - F2 - phase space
PX285 - F3a - particle in 1D
PX285 - F3b - pendulum
PX285 - F4 - gyroscope
PX285 - F5 - central forces - particle approaching the sun
G - normal modes and small oscillations
PX285 - G1 - inertia tensor
PX285 - G2 - stiffness matrix
PX285 - G3 - derivation from examples
PX285 - G4 - attached particles on springs
PX285 - G5 - non-diagonal inertia matrix
PX285 - G6 - summary
PX285 - G7 - example
PX285 - G8 - diatomic molecule
PX285 - G9 - triatomic molecule
fluid dynamics
H - introduction to fluids
PX285 - H1 - fluids
PX285 - H2 - fluid approach
PX285 - H3 - mechanical perspective of fluids
PX285 - H4 - newton's law of viscosity
PX285 - H5 - fluid element
PX285 - H6a - stream line
PX285 - H6b - example of a flow
PX285 - H6c - example in a cylinder
PX285 - H7 - quantifying the effects of viscosity
I - navier-stokes equation
PX285 - I1 - conservation of mass
PX285 - I2a - conservation of momentum
PX285 - I2b - advective derivative
PX285 - I3 - pressure equation
PX285 - I4 - core equations
PX285 - I5 - initial and boundary conditions
J - some approximate solutions
PX285 - J1a - bernoulli's principle from conservation of energy
PX285 - J1b - bernoulli's principle from navier-stokes equation
PX285 - J2 - hydrostatic limit and archimedes' principle
PX285 - J3 - water drain
PX285 - J4 - venturi pipe
PX285 - J5 - stagnation point
PX285 - J6 - pitot pipe
PX285 - J7- surface waves
PX285 - J8 - aerofoil
K - circulation and vorticity
PX285 - K1 - vorticity
PX285 - K2 - kelvin's circulation theorem
L - potential flows
PX285 - L1 - potential flows
PX285 - L2 - potential dipole
PX285 - L3 - potential flows involving cylinders and aerofoils
PX285 - L4a - lift and circulation - magnus effect
PX285 - L4b - aerofoil
PX285 - L5a - vortex lines
PX285 - L5b - interacting vortex lines
PX285 - L6 - potential flow over a wing
PX285 - L7 - boundary layers
PX285 - L8 - aerofoil lift