Unformatted text preview: cular distance from a focus to the
asymptote
Note that
and hence the lack of
absolute values on compared to elliptical
case Kinetic
Energy: Relationship between impact parameter, initial
velocity, and angle between asymptotes
(scattering angle): Potential
energy: Chapter 8: Many Body Systems:
Equation
of
motion: Total
energy: Internal conservative forces: Euler
angles Three rotations are sufficient to rotate a body
to its principal orientation
0. Start with
1. Rotate by angle about axis
2. Rotate by angle Lagrangia
n: axis 3. Rotate by angle about axis Generalized coordinates of particles:
Kinetic
energy Rocket emitting matter at constant velocity u
relative to rocket with speed v. For a symmetric body, last rotation is
unnecessary
Kinetic energy in terms of rate of change in
Euler angles: Map coordinates: Rockets about Rotation
with
misalignm
ent with
principal
axis: Chapter 9: Rigid Bodies Stable if Constraints or , in which case and 6 more degrees of freedom
describes position of all particles
takes 3 degrees of
freedom (trivial for isolated system) Chapter 10: Lagrangian Mechanics Angular
velocity,
angular
momentu
m, and
moment of
inertia Most
general
case: Conservative force: Velocitypotential:
Principal
moments
of inertia Principal axes: Kinetic energy: Most general force: Chapter 12: Hamiltonian mechanics
Definition:
Dissipative force:
 Examples: Damped harmonic oscillator:
Derivatives
of :
Charged particle in EM field:
Natural
system (not
forced): Motion of
a
stretched
string: Action integral: In general, To apply, just plug into definition and
then make sure only depends on
and ....
View
Full Document
 Fall '08
 MoChen
 mechanics, Energy, Force

Click to edit the document details