Two-body motion with a central potential
Translation from general expressions:
gravitational force:
based on FW-4
particle with the
reduced mass subject to
a central force
Everything we have derived f
Classical Mechanics
P 521, Fall 2013
Radovan Dermisek
Indiana University, Bloomington
Notes based on:
Fetter and Walecka, Theoretical Mechanics of Particles and Continua,
Chapters 1-6
1
Basic Principl
Falling particle:
solution as an expansion in !
the deflection is Eastward
for a 100m drop the equatorial deflection is 2.2cm
57
Horizontal motion:
Coriolis force deflects moving objects to
the right
Homework set - 4
due on Wednesday, October 9, 11:00am
1) Problem 3.1 from Fetter and Walecka
2) Problem 3.5 from Fetter and Walecka
3) Problem 3.6 from Fetter and Walecka
4) next page
1
4) Imagine a s
Homework set - 9
due on Wednesday, December 4, 11:00am
1) A nasty bacterium in the shape of a spheroid with principal axes b, b, a and
uniform density is spinning in free space about its axis of symme
Homework set - 3
due on Wednesday, September 25, 11:00am
1) Problem 2.4 from Fetter and Walecka
2) Problem 2.5 from Fetter and Walecka
3) Problem 2.1 a) from Fetter and Walecka
b) What is the trajecto
Homework set - 1
due on Wednesday, September 11, 11:00am
1,2,3) Problems 1.4, 1.6 and 1.10 from Fetter and Walecka
4) Imagine a particle of mass m moving in a perturbed attractive Coulomb
potential:
k
Homework set - 5
due on Wednesday, October 23, 11:00am
1) Problem 3.10 from Fetter and Walecka
2) Problem 3.11 from Fetter and Walecka
3) Problem 3.15 from Fetter and Walecka
4) Problem 3.17 from Fett
Homework set - 2
due on Wednesday, September 18, 11:00am
1) Problem 1.7 from Fetter and Walecka
2) Problem 1.13 from Fetter and Walecka
3) Problem 1.14 from Fetter and Walecka
hint: do first the probl
Homework set - 8
due on Wednesday, November 20, 11:00am
1) Problem 5.2 from Fetter and Walecka
2) Problem 5.5 from Fetter and Walecka
3) Calculate the moments of inertia of a spheroid with principal a
Rotating Coordinate Systems
based on FW-6,7,8
Sometimes it is useful to analyze motion in a non inertial reference frame, e.g.
when the observer is moving (accelerating).
Inertial frame:
orthonormal c
Falling particle:
solution as an expansion in !
the deflection is Eastward
for a 100m drop the equatorial deflection is 2.2cm
57
Horizontal motion:
Coriolis force deflects moving objects to
the right
Two-body motion with a central potential
based on FW-4
Everything we have derived for the motion
of a particle with mass m subject to a
central force:
can be directly (with small modifications) applie
Two-body motion with a central potential
based on FW-4
Everything we have derived for the motion
of a particle with mass m subject to a
central force:
can be directly (with small modifications) applie
Central Forces
Keplers second law:
based on FW-3
Motion of a particle with mass m subject
to a central force:
An imaginary line drawn from each planet to the Sun sweeps
out equal areas in equal times.
Cross section:
incident flux
(number of particles crossing unit transverse area per unit time)
differential cross section
event p = elastic scattering through a
deflection angle between # and # + d#:
Cross section:
Hyperbola:
incident flux
constant difference in distance from two foci
located at x=+f and x=-f:
(number of particles crossing unit transverse area per unit time)
left branch
r
"
differ
Rotating Coordinate Systems
based on FW-6,7,8
Sometimes it is useful to analyze motion in a non inertial reference frame, e.g.
when the observer is moving (accelerating).
Inertial frame:
orthonormal c
Classical Mechanics
P 521, Fall 2013
Radovan Dermisek
Indiana University, Bloomington
Notes based on:
Fetter and Walecka, Theoretical Mechanics of Particles and Continua,
Chapters 1-6
1
Basic Principl
Cross section:
incident flux
(number of particles crossing unit transverse area per unit time)
differential cross section
(constant of proportionality)
event p = elastic scattering through a
deflectio
Central Forces
based on FW-3
Motion of a particle with mass m subject
to a central force:
conservative
xF=0
)
no torque, r x F = 0
l = r x p = const.
(motion is planar, perpendicular to l)
It is conve
Homework set - 7
due on Friday, November 8, 11:00am
1) Problem 4.1 from Fetter and Walecka, only parts c) and d)
2) Problem 4.3 from Fetter and Walecka, only parts d), e) and f)
3) Problem 4.2 from Fe