Hence 1 cm is 1.1 pF. Since the RC time constant is still in seconds, (2.99792458)2 1011
Ohms is 1 sec/cm.
Since the resistance is given by R = L/A where is the resistivity, L is the length and
A is the area, the units for the resistivity are seconds. Thi

J. Peraire S. Widnall
16.07 Dynamics
Fall 2008
Version 2.0
Lecture L30 3D Rigid Body Dynamics: Tops and Gyroscopes
3D Rigid Body Dynamics: Euler Equations in Euler Angles
In lecture 29, we introduced the Euler angles as a framework for formulating and sol

J. Peraire S. Widnall
16.07 Dynamics
Fall 2008
Version 2.0
Lecture L14 Variable Mass Systems: The Rocket Equation
In this lecture, we consider the problem in which the mass of the body changes during the motion, that is,
m is a function of t, i.e. m(t). A

16.851 Assignment #1, 2003-09-17
Problem Statement
Motivation
The design of a spacecraft power subsystem is an important driver for the mass, size, and
capability of the spacecraft. Every other spacecraft subsystem is affected by the power
subsystem, and

Problem
(25 points)
1.1) Consider a pendulum of mass m/2 at rest suspended by a massless rod of length L from a
frictionless pivot in the presence of gravity, shown in a). Use small angle approximation for the
subsequent motion of the pendulum, < 1.
a) A

1. (9 points) What is the maximum acceleration which can be given to the cart
without tipping over the container with dimensions h and b? Assume that friction
is large enough to prevent any slipping.
b
g
h
a
2. (9 points) A pendulum consists of a massless

Problem 1
In this problem, assume that the flow is inviscid and two-dimensional.
a) Determine the lift and drag coefficient for a flat plate at M = 4 , = 4 degrees.
b) Determine the lift and drag coefficient for a flat plate at M = 4 , = 8 degrees.
.
c) U

7. The Station must be capable of sustaining launch loads, as well as maintaining
a safety factor of 3.
8. It will cost ~$10K per kilogram to final orbit.
9. Assume a Research, Development, Test and Evaluation (RDT&E) cost of
$200M.
What is the best mater

S Widnall
16 07 Dynamics
Fall 2008
Version 1 0
Lecture L18 Exploring the Neighborhood: the Restricted
Three Body Problem
The Three Body Problem
In Lecture 15-17, we presented the solution to the two-body problem for mutual gravitational attraction.
We wer

Finally, the user inputs much power the satellite uses during daylight and eclipse and the mission
lifetime.
Using the equations from page 546 of SMAD, the first module calculates the T (the amount of
time the satellite must be in view of the ground stati

15.
Gravitational Radiation
Gravitational waves also come from time varying mass quadrupoles. The formula for
radiation from a binary star is
2
2
dE
32G4 M1 M2 (M1 + M2 ) 1 + 73 e2 37 e4
24
96
=
dt
5c5 a5
(1 e2 )1/2
(326)
Taking e = 0 for simplicity this

Data Mass Storage Design Trade-Off
Approach
The aim of this trade-off is to show the relationship between the data rate chosen (if
given frequency, data rate can be calculated for the link design equation 13-4 in
SMAD) and mass of the data storage needed