Welcome to
dr Alfred St�pniewski'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.
Now You can download
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 St�pniewski -my home address-
or via e-mail: stepniew@safona.tuniv.szczecin.pl
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