Vector representations

"Double-A" wrote in message
om...
"Donald G. Shead" wrote in message
om...
There are two 'kinds' of motion: 'Inertial' motion [vi*t],
and 'Forced' [accelerated] motion [at²/2]: Which
together [vi*t + at²/2] make up the 'Resultant'
motion that we "see". These are representable,
TO SCALE as vectors: The vectors may extend in any
direction; including backward [-] and forward [+]:


o---------------|----------------------|
l = vi*t s = at²/2
o---------------------------------------|
d = l + s = vi*t + at²/2


And if you add a constant for the starting position, such as x_0, then
the formula

d = vi*t + at^2/2 + x_0

will give you the exact milepost you have reached on the highway you
are travelling on!

Double-A

Assuming _any_ change in position [d] has a starting point; another term in
the equation is superfluous. The equation is complete without x_0; which
would just shift the starting and ending positions equally anyways; unless
it's zero!

You are trying to sneak the calculus in aren't you(;-?

Actually, for most motion problems; assuming a body is at rest initially,
and we want to move it to another (new) position, some distance [d] away,
and _leave it stopped there_; there will be three parts to the problem: An
initial accelerating part, which starts the body moving; a middle some times
energy wasting inertial part, and a decelerating stopping part:

Ideally we might want to keep the middle part as brief as we can to avoid
it's non-productive duration; especially if there is friction; but I've
showed a "vector" [l = v*t] for it to make the picture more complete;

|starting position
o----------|------------|--------o|ending
| s = at²/2 l = v*t -s = -at²/2 position
o---------------------------------- |
d = s + l - s = at²/2 + v*t + (-at²/2)

_My_ "vectors" are representative of _motion components_: I've showed
straight lines because I'm unable - or don't know how - to send curves; and
motion components are often curved for numerous reasons. The main curves of
motion consist of tangents, elliptical arcs and involutes [to connect them].

Sending up satellites too requires an initial accelerating involute part to
initiate the circular or elliiptical orbit, which is usually placed beyond
the reach of atmospheric friction; so that the middle part is usually not
wastful, but is the productive part, and may be quite extensive; then
finally a decelerating involute part brings it into Earth's atmosphere
again, where it burns up, and/or falls to the surface.

But the principle is the same:

The two 'kinds' of motion: 'Inertial' motion [vi*t, and/or v*t],
and 'Forced' [accelerated, and/or decelerated] motion [at²/2]: Which all
together combine to make up the 'Resultant' motions [d/t] that we "see", and
are all representable, TO SCALE as vector components; which may extend and
curve in any direction; including backward [-] and forward [+]...

Ask a "drafter" to draw up a few samples if you want to see for yourself.

"Donald G. Shead" wrote in message
m...

Ac.. .. ..

BS Filter Activated.

"Ronald Stepp" wrote in message
...
"Donald G. Shead" wrote in message
m...

Ac.. .. ..

BS Filter Activated.


Too bad; that means no more sending for yooh(;^!

"Donald G. Shead" wrote:

Actually, for most motion problems; assuming a body is at rest initially,
and we want to move it to another (new) position, some distance [d] away,
and _leave it stopped there_; there will be three parts to the problem: An
initial accelerating part, which starts the body moving; a middle some times
energy wasting inertial part, and a decelerating stopping part:
[snip]

Idiot ****Head cannot do high school physics. Tell us how an inertial
trajectory "wastes energy," ****Head. Newton's First Law: "An object
at rest tends to stay at rest and an object in motion tends to stay in
motion with the same speed and in the same direction unless acted upon
by an unbalanced force."

BTW, ****Head, Newton's first law of motion contains the same
information as Galileo's explanation of inertia.

http://scienceworld.wolfram.com/phys...sFirstLaw.html

****Head, ****Head, ****Head, ****Head...

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

"Uncle Al" wrote in message
...
"Donald G. Shead" wrote:

Actually, for most motion problems; assuming a body is at rest
initially,
and we want to move it to another (new) position, some distance [d]
away,
and _leave it stopped there_; there will be three parts to the problem:
An
initial accelerating part, which starts the body moving; a middle some
times
energy wasting inertial part, and a decelerating stopping part:
[snip]

Cut

Idiot...cannot do high school physics. Tell us how an inertial
trajectory "wastes energy,"
Cut
Less'n it's high enough it will loose energy to atmospheric friction.

Newton's First Law: "An object
at rest tends to stay at rest and an object in motion tends to stay in
motion with the same speed and in the same direction unless acted upon
by an unbalanced force."

BTW,
Cut
Newton's first law of motion contains the same
information as Galileo's explanation of inertia.

http://scienceworld.wolfram.com/phys...sFirstLaw.html

Cut A few insults

I know, and Newton gave credit where it was due...

"Donald G. Shead" wrote in message om...
"Double-A" wrote in message
om...
"Donald G. Shead" wrote in message
om...
There are two 'kinds' of motion: 'Inertial' motion [vi*t],
and 'Forced' [accelerated] motion [at²/2]: Which
together [vi*t + at²/2] make up the 'Resultant'
motion that we "see". These are representable,
TO SCALE as vectors: The vectors may extend in any
direction; including backward [-] and forward [+]:


o---------------|----------------------|
l = vi*t s = at²/2
o---------------------------------------|
d = l + s = vi*t + at²/2


And if you add a constant for the starting position, such as x_0, then
the formula

d = vi*t + at^2/2 + x_0

will give you the exact milepost you have reached on the highway you
are travelling on!

Double-A

Assuming _any_ change in position [d] has a starting point; another term in
the equation is superfluous. The equation is complete without x_0; which
would just shift the starting and ending positions equally anyways; unless
it's zero!

You are trying to sneak the calculus in aren't you(;-?


Now, I wouldn't do that to you, would I? Fact is, I don't care
whether you use calculus or not. Like I said before, it's just a
tool. You can make up your firewood with the old bucksaw just as well
as with the chainsaw. It will just take a little more time and
effort, that's all.

Actually, I kind of like the way you hammer away at the fundamentals.
A lot of people memorize a lot of higher math, but forget what the
hell it's all about. Never hurts to keep reviewing, and questioning,
the fundamentals.

Double-A

"Donald G. Shead" wrote in message
...

"Ronald Stepp" wrote in message
...
"Donald G. Shead" wrote in message
m...

Ac.. .. ..

BS Filter Activated.


Too.. .. ..

Dense Moron Filter Activated.

"Double-A" wrote in message
om...

Actually, I kind of like the way you hammer away at the
fundamentals.
A lot of people memorize a lot of higher math, but forget what the
hell it's all about. Never hurts to keep reviewing, and
questioning,
the fundamentals.

I would prefer the fundamentals be hammered home by someone who isn't
trying to push his interpretations of physics with them...
fundamentals aren't much good if they aren't accurate.

"Ronald Stepp" wrote in message
.. .
"Donald G. Shead" wrote in message
...

"Ronald Stepp" wrote in message
...
"Donald G. Shead" wrote in message
m...

Ac.. .. ..

BS Filter Activated.


Too.. .. ..

Dense Moron Filter Activated.


NOW; you'll never get out(:-)