Unformatted text preview: se at
;
: Solution: Sum of impulse forces at time
Trajectory (eliminate from above):  Arbitrary force (analogous to arbitrary
periodic force above) Moments and
angular
momentum: We used this example quite a lot in our
HW
Torque: (Moment of a force about the
origin)
Angular momentum: (Moment of
momentum about the origin)  Wasn’t really covered in class… see
example on page 39.
is first time at which force becomes
nonzero Chapter 3: Energy and Angular Momentum
Energy
conservation
in 3D Conservative force: Projectiles with no air drag:
Equation of motion: Central
forces:
 Force is
always
parallel to
position
vector
Cylindrical
and spherical
coordinates  Motion is confined to a plane
Rate of area sweeping out by position
vector is constant Split into components: Solution: Calculus of
variations: Stationary values of an integral satisfy EulerLagrange equation: Maximum height, flight time, and range: In general Projectiles with air drag:
Equation of motion:
Split into components: Hamilton’s
principle;
Lagrange’s
equation may depend on more things Lagrangian function in any coordinate
system: Action integral: Inverse
square
law: Equations of motion:  Can be used to find
the force in the which is Generalized momenta and forces (not
necessarily the same as momentum and
force): Chapter 4: Central Conservative Forces
Isotropic
harmonic
oscillator Equation of motion: Energy
conservati
on: In g...
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 Fall '08
 MoChen
 mechanics, Energy, Force

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