Welcome to
dr Alfred Stępniewski's
d'Alembert's supplemented and generalized principle
home page.
I deeply hope that presented here work will
be useful in showing basic mechanics laws in a very different light...
While conducting lectures in mechanics I've noticed many
different principles explantations which conducted me to supplementing
and generalizing of d`Alembert's principle and to supplementing of the
Newton's laws, which I'd like to present now.
SUMMARY
of document dalnewsb.zip
In this article, the elucidation of the inconsistency of the
type 3 = 6 met at the derivation of Euler's equations which describe the
rotation about a fixed point of a rigid body is presented. To this end,
the dynamic balance law called d'Alembert's supplemented principle
U [ P , A ; r(t) ] = 0
A = -ma for t = to r = ro , v = vo
provided that
P + A = 0 ,
so we have:
ma = P
for t = to r = ro , v = vo
and
Mo(P,A)= r x P + r x A = r x (P+A) = r x 0 = 0
as well as
-r x A = r x ma = d(r x mv)/dt = dK/dt = r x P = M ,
has been formulated which as a generalization of Newton's supplemented third
law
U [ RBA , RAB ; rC ] = 0
provided that
RBA + RAB = 0
and
Mo(RBA , RAB) = rC x RBA + rC x RAB =
= rC x ( RBA + RAB) = rC x 0 = 0 ,
has been derived directly from experience. Generalizing this law to
any physical media, the primary principles of dynamics of those media have
been corrected and the dynamics of multiatomic gases has been formulated.
However Newton's second multidimensional law supplemented by constraints
equation in Riemann's multidimensional space leads also to six dynamic
equations of the general motion of a rigid body as well as to dynamic equations
of motion in a covariant from which are Appell's equations of any holonomic
and inholonomic material system in Riemann' s subspace of space.
The d`Alembert's supplemented and
generalized principle as well as the supplemented Newton's second and third
law as basic laws of clasical mechanics.
"The d`Alembert's principle..." is compressed
(to file dalnewsa.zip in Polish language
and dalnewsb.zip in English language) and
it's written in AmiPro or to file dalnesaw.zip in Polish language
and dalnesbw.zip in English language and
it's written in Word
CONTACT:
I'll be glad to receive any comments. Correspondence (unfortunatly
only in Polish) You can send to:
dr Alfred Stępniewski -my
home address-
or via e-mail: stepniew@safona.tuniv.szczecin.pl
Home page was set on: 21 May 1996
Last actualization: 21 December 1996.
