DOC.

1

MECHANICS LECTURE NOTES

1

Doc.

1

Lecture

Notes

for

Introductory

Course

on

Mechanics

at

the

University

of

Zurich,

Winter

Semester

1909/1910

[18

October 1909-5 March

1910][1]

Mechanics

is

the

science

of motion of

ponderable matter.

It

establishes

the conditions

[p.

1]

under

which

the motion of

matter

ceases

(statics).[2]

It

seeks to

reduce the

manifold

phenomena

of

motion to

the

smallest

possible

number of

elementary laws

of

the

simplest

possible

form,

from

which

it

seeks

to

reconstruct

the

more complicated phenomena.

I.

Mechanics of

the

Material

Point

We shall

first

discuss

the motion of

a

body

whose

dimensions

are

of

no

importance

in

the

motions

we

will

discuss,

that

is,

can

be

regarded

as

»

small.

While in

motion,

such

a

body

will,

in

general,

carry

out

rotations and

change

its

shape.

But

we

disregard

these

circumstances,

that

is,

treat it

as

if

it

were

pointlike;

we designate

it

as a

"material

point."

Before

we

investigate

the motion of

a m.

p.[3]

as a

function

of the

motive

causes,

we

must discuss

the

means

and the

auxiliary

quantities

that

we use

in

order

to describe

the

motion of

an m.

point.

A.

Kinematics of

the M. P.

One

cannot

speak

of the motion of

a body

(and

hence

also

of

a m. p.)

in

and

for

itself,

[p. 2]

but

only

of

a

relative motion of

bodies with

respect

to each

other. If

we

wish to

describe

the motion of

an m. p., we

must

describe its

motion

with

respect

to

a

second

body.

For

the latter

we

choose

a system

of

3

mutually

perpendicular

rigid

rods.

(Coordinate

system).

We

conceive

of

times

as

being

measured

by

an

arbitrary

clock,

in

that

we

assume

that

means are

available

for

ascertaining

the

readings

of the

clock

that

are

simultaneous

with

particular

individual

positions

that the

m. p. assumes

during

its motion.

Obviously,

the motion of the

body

m. p.

is

given

if

the coordinates

x, y, z

are

given

with

respect

to

the

c.s.[4] as a

function

of

time.

Equations

of the

following type

obtain

here:

x

=

p

(t)

y

=

iK0

*

=

X(0

Rectilinear motion

(a)

uniform