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: g2news2.google.com!news3.google.com!feeder.news-service.com!94.75.214.39.MISMATCH!aioe.org!.POSTED!not-for-mail From: "Nasser M. Abbasi" Newsgroups: comp.lang.ada Subject: Re: Fun with C Date: Mon, 25 Apr 2011 23:58:37 -0700 Organization: Aioe.org NNTP Server Message-ID: 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> Reply-To: nma@12000.org NNTP-Posting-Host: tUYQ4Ty9mMw9Pdc8TJRFQA.user.speranza.aioe.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Complaints-To: abuse@aioe.org User-Agent: Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US; rv:1.9.2.15) Gecko/20110303 Thunderbird/3.1.9 X-Notice: Filtered by postfilter v. 0.8.2 Xref: g2news2.google.com comp.lang.ada:20024 Date: 2011-04-25T23:58:37-07:00 List-Id: 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. 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. One can use GR equations (10 highly non-linear coupled PDE's [1]) to describe the equation of motion of the pendulum, and after making all the approximations needed to account for slow motion of the pendulum blob (relative to speed of light :), its small mass (relative to earth) hence small space-time curvature, and after numerically solving them, one will get the same results within a tolerance of error that can be ignored for all practical reasons, as the one we get with a simple model based on F=ma and small angle approximation. So, you can use GR to solve the pendulum problem, and I can use F=ma, and in the end, we will get the same results for all practical reason, except I used a very simplified model, and you used a very complicated model, of the same physical problem. What matter is if the result of the model agrees well to the observed behavior. Any way, this is how engineers look at things :) --Nasser [1]http://en.wikipedia.org/wiki/Einstein_field_equations