From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-0.3 required=5.0 tests=BAYES_00, REPLYTO_WITHOUT_TO_CC autolearn=no autolearn_force=no version=3.4.4 X-Google-Thread: 103376,a9b0810d3106d9b8 X-Google-NewGroupId: yes X-Google-Attributes: gida07f3367d7,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII-7-bit Path: g2news1.google.com!news1.google.com!goblin2!goblin1!goblin3!goblin.stu.neva.ru!news.weisnix.org!newsfeed.ision.net!newsfeed2.easynews.net!ision!newsfeed.arcor.de!newsspool4.arcor-online.net!news.arcor.de.POSTED!not-for-mail From: "Dmitry A. Kazakov" Subject: Re: Fun with C Newsgroups: comp.lang.ada User-Agent: 40tude_Dialog/2.0.15.1 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Reply-To: mailbox@dmitry-kazakov.de Organization: cbb software GmbH References: <4b5748dc-60fa-4cec-a317-054626e9a1ca@d19g2000prh.googlegroups.com> <1908th3tyz101.1f6c5w8t9mggy.dlg@40tude.net> <2118e788-7b3e-4d25-8d0f-5e60498e3a3b@cu4g2000vbb.googlegroups.com> <1hnl95prvrt6i$.1s675gncbjxsu$.dlg@40tude.net> <5d44db50-ceff-4f4d-8bc7-714f31fbca06@hd10g2000vbb.googlegroups.com> <1uthrsrabx8di$.8i74uk28axo0.dlg@40tude.net> <84b83223-e191-4912-8f73-318deb4dd783@d19g2000prh.googlegroups.com> <1j2bi0982bjcs.1beq9xn9za9yb$.dlg@40tude.net> <9j18r6hrlf06adfv4rdothhdrjmfdrmeno@4ax.com> <1qe52ny88vlk9$.hcf0wgd0xcmh.dlg@40tude.net> <117x5uepxzqrn$.zu65rz3wdey9.dlg@40tude.net> <10wrcep2z88z3$.1q3jmf2y5a0qn.dlg@40tude.net> <356b1c5c-9b6e-488b-a31a-6e1d15082f2c@k22g2000yqh.googlegroups.com> Date: Tue, 26 Apr 2011 10:39:37 +0200 Message-ID: NNTP-Posting-Date: 26 Apr 2011 10:39:39 CEST NNTP-Posting-Host: 93cd89ac.newsspool3.arcor-online.net X-Trace: DXC=\D`c]:GF7Bg<6cDJZfMd_cMcF=Q^Z^V3h4Fo<]lROoRa8kF On Mon, 25 Apr 2011 23:58:37 -0700, Nasser M. Abbasi wrote: > On 4/25/2011 11:18 PM, Dmitry A. Kazakov wrote: >> On Mon, 25 Apr 2011 13:46:40 -0700 (PDT), Maciej Sobczak wrote: >> >>> On Apr 25, 9:09 am, "Dmitry A. Kazakov" >>> wrote: >>> >>>> No, it is a catastrophic approximation because linear system cannot >>>> oscillate. >>> >>> What? A simple hanging spring can oscillate while being purely linear. > >> That system is not linear. > > One should really attribute linearity or not to the equations that > describes the motion of the system. > The pendulum itself is just the pendulum, and saying that > the pendulum itself is not linear, I do not think is very exact, > but I know you meant the equation of motion when you said that. > > So, now lets talk then about the equation of motion. > > Again, under small angle approximation, the equation of motion > of the pendulum can be approximated to linear one. When > the angle is large, then the approximation is not a good one, > and one must use the non-linear equation of motion to make > better prediction of its motion. > > So, we back to square one. I am not. The Ptolemy's system is a fair approximation of planet movement. Moreover, it is asymptotically correct, and mathematically represents the first ever example of harmonic analysis (a very important tool in engineering). All that does not make it "right". The Copernican system, which is plain numerically wrong, and also wrong from the relativity theory point of view, is taught as a "truth". You cannot ignore the context. > We make a mathematical model > of the physical problem, and if the approximation we make > to this model seems to give good results for our needs, then > that is the model we should use. Yes, except the cases where results cannot be verified, and discarding the context makes anything unverifiable. Models you are talking about exist in a larger context taken for granted. For example, you presume that laws do not change with the time etc. Just consider models where time would be a function of some system parameters. There is an infinite number of models fitting given system. Among these only models consistent with more fundamental laws and principles are considered. Empiric models are subordinate. You can consider deploying such a model (like F=ma) only after stating its conformance to a more fundamental theory (the relativity theory). As an engineer you also must show the boundaries within your empiric model can be used. > Any way, this is how engineers look at things :) You mean those programming in C? (:-)) -- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.de