ЗйлеровьI рещения задчи о поступательно вращатльном движени трех твердьени трех твердьх тел

I I (, 1976). I :I I I I I I I (I) I I . I . , I I .

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Euler solutions in the problem of the translatory-rotary motion of three rigid bodies

The present paper is a continuation of the article (Vidyakin, 1976) in which we proved the existence of Lagrange (triangle) solutions in the general problem of the translatory-rotary motion of three absolutely rigid bodies.In particular, we have found the conditions for the existence of Lagrange solutions in the case when all the bodies possess a symmetry with respect to three mutually perpendicular planes both in respect to the distribution of matter and in respect to the outward form. In this case the bodies effect simple translations along with the centres of the masses without rotation (in Lyapunov's system of coordinates).If the rigid bodies possess a symmetry in respect to the axis and to the plane, perpendicular to this axis, then the Lagrange solutions of the three floats (Duboshin, 1973), three spokes (Kondurar, 1974), three shafts (Vidyakin, 1976) types are admitted, as well as the solutions in the cases of combinations of the float, spoke and shaft-bodies (Vidyakin, 1976).Those solutions exist of certain conditions, imposed on the structure, orientation and rotation of the bodies, are observed.In the general case (there) exist particular solutions which we have termed as Near-Lagrangian.The present paper is to prove the existence of Euler (rectilinear) solutions in the problem of the translatory-rotary motion of three rigid bodies, assuming that the elementary particles of the rigid bodies are mutually attracted according to the Newtonian law.In particular, we have found the conditions for the existence of Euler solutions in the case when all the bodies possess a symmetry in respect to three mutually perpendicular planes both in respect to the distribution of matter and in respect to the outward form. In this case the bodies are so disposed in the uniformly rotating coordinate system that two symmetry planes concur while the centres of the masses are disposed on one straight line.In particular, if the bodies possess a symmetry in respect to the axis and to the plane perpendicular to this axis, then the Euler solutions of the three floats (Duboshin, 1973), three spokes, three shafts types as well as solutions in the cases of combinations of float-, spoke- and shaft-bodies and spheres, either homogeneous or possessing a spherically symmetric distribution of densities, are admitted.The paper gives exact solutions for the cases when the attraction force function of the bodies has an approximate expression.

     

The ratios I(K1)/I(H1) and I(K3)/I(H3) of ca II as diagnostics of the chromosphere above sunspots

The ratios I(K ₁)/I(H ₁) and I(K ₃)/I(H ₃) were calculated from four semi-empirical models of sunspot umbra. We determined the dependencies of both ratios of such parameters as temperature gradient and atmospheric opacity. A certain influence on the expected ratios I(K ₁)/I(H ₁) and I(K ₃)/I(H ₃) can also come from the FIP effect provided it exists in the chromosphere above sunspot umbra. Theoretical and observed values of I(K ₁)/I(H ₁) and I(K ₃)/I(H ₃) are compared. It is shown that for one of the sunspots we observed, the values obtained for the ratio I(K ₁)/I(H ₁) cannot be explained in terms of existing umbra models.     

Infrared Spectroscopy from San Fernando Observatory: He I 1083 nm, O I 1316 nm, and Fe I 1565 nm

Imaging spectroscopy of the Sun was carried out at the California State University Northridge San Fernando Observatory using an InGaAs near-IR video camera. Using the Sii 1082.71 nm and Hei 1083.03 nm lines the Evershed effect is measured simultaneously in the photosphere and the chromosphere for three sunspots; the speed of the Evershed flow is measured to be between 3 to 8 times greater in the Hei line than in the Sii line, and the direction is radially inward in the chromosphere and outward in the photosphere. Telluric absorption lines prevented a meaningful measurement of Oi 1128.7 nm limb emission, but an upper limit of 20×10^–3 B is measured for chromospheric limb emission at Oi 1316.3 nm. Zeeman splitting in Fei 1564.9 nm was observed in six sunspot umbrae, and a linear relationship between magnetic field and umbral continuum intensity is confirmed.     

BL Lac天体和FR—I射电星系的统一模型（I）

从射电结构的角度评述了ＢＬＬａｃ天体和ＦＲ－Ｉ射电星系的统一模型的最新进展，内容包括射电结构，延展射电光度（Ｐｅｘｔ），最大角尺度（ＬＡＳ），射电核主导系数（ｆ）的比较以及对相对论聚束的测试。最新的射电观测资料表明ＸＢＬｓ是介于ＦＲ－Ｉ和ＲＢＬｓ之间的过渡型天体，这对ＢＬＬａｃ天体是聚束的ＦＲ－Ｉ射电星系提供了一个很好的证据。     

I.低频甚低频传播突然扰动

1997年 9月 日 l5 17 l9 20 21 开始START (UT) 0205 0348 0144 0030 0416极大MAX(UT)02170406015300490420结束END(UT)0315050003050130U0515级别IMP SPA LF如(拜s)△乳(科s) 一2 .9一3。2 一0.9一1.0 一3 .8一4.5 一0。8一0。6 一1 .5一1.7 SPA SFA VLF LF△,(拌s)△A(dB) 一+1 .1 一一1.8 一一3.2,十0.4 一+1.7 一一一3。O一一一夕︼..几O‘﹃.孟,.上一++,工,万人、二004703220315005403350328O120U05070455一0.8一2 .6一2 .0一0。9一2.9一2.2+0 .9一3 .8一4。4,曰尸O︵b心‘,﹄今‘I.低频甚低频传播突然扰动~~…     

I.低频甚低频传播突然扰动

2003年 9月 日 开始盯)ARI,SPALFSPA SFAVLFLF(UT)娜(娜)△肠(卢)娜!(娜)从(dB)划IMP教END(UT)02170302012501010125022803080132010701520250U034()02230155U0250 +1 .3 +0 .8一1 .7,+1.1 一1 .2 一3 .5︸、︸︵吕70沙OJOC︸八J .1‘.1一一一一一尹O一X︸0 工f︸八U00八J,12 一一一一一一一一月.上月l,‘,l曰.几︸日nU 4 工f︶7曰.且J.几‘.1 J.且心l一2 .1,+2.3 一1 .1 一1 .7 0 一0 .7‘J 70沙曰急月了内Jn︸,上,且n︸一一一一一27护00了nU八J一U峭1 01人 一一一一一 一一一门乙月.几,几J.l曰.几0349022704360718oo2…     

I.低频甚低频传播突然扰动

么扣3年 10月 日SPA1万班叭班叭协万廿仰(娜)娜(”)娜(脾)队(dB)划皿棘加(Ur)QU 0 QU咤甘︵”甘产O七J JO砚曰2+一++一夕00一吕内J几」夕00才自J 102一一一一一气甘7一月︸八U JO4咤甘2月J,二一一一一一一+一++傀曰月J 22‘.几0710加乃08U0210U羔(UT)0628姗0113 07250037.j RU,‘护O气甘,三月J久曰‘二咤曰一++++24夕0 801几4,占04一一一一一06月1︸,几内」,人月J心l‘.1内,︸一一一一一030103490501024003490315U044505230328U以3口D1211一2一一9 .3一4 .3一4.4一7 .5一14 .1一5 .3,+7.4 +8 .0 +8 .8 一6 .4,+17一6 .8,+17.29…     

I.低频甚低频传播突然扰动

1994 12 开始START (UT) 0207 0327 0637 0242 0539 0119 0436极大MAX(UT)0212033506500259054401450441结束END(UT)02390400075003100620D02350530级别IMP1l一2l一3+1+1+ SPA LF△甲(尸)仰(仰) 一O。8一1。1 一0。4一0。5 一2。7一4。9 一O。6一0。7 一6。6一9。9 一2。1一Z。7 一1。5一2。l SPA SFA VLF LF△,(拌s)△A(dB) 一一l。7 一一l。5 一一3。3,+O。7 一O 一一12.0,+10.1 一一1。0,+1.0 一一O。9年月日09 n 12 13 14 1819I.低频甚低频传播突然扰动~~…     

I.低频甚低频传播突然扰动

1996年 11月 日 24 2生 25 名5 25 25 艺5 开始START (UT) 0402 0600 0013 0055 0240 0408 0515极大MAX(UT、O生09061000230 10002生9041405之5结束END(UT)0432U06400200D01150310043006之O级别IMP SPA 工_F么甲(拜5少△甲。‘拼5/ 一母.3一0.屯 一弓是一0.了 一三.4一10.忿 一‘.3一0.生 一07一0.沙 一‘少.3一口.之 一上3一1.日SP二、 V工JF么甲(拼、)1一1一O一1一1一1一l 共尸A 遏F么:气火dB一三.1弓3J论铺I.低频甚低频传播突然扰动~~…     

I.低频甚低频传播突然扰动

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I.低频甚低频传播突然扰动

2001年 5月 日 开始幻沐RT(UT)SPALF任叭牙AVl万1万铆(娜)如(户)邹(娜)△A(dB)划肥教咖(UT)0156似价0631仪论301穷似似021606390102似01似的勺似30U价30似50D0240D1123一2 一1 .4一1 .5一4 .1一万.8一5.1 4 .6 2.3 一1 .7一3 .5, 1 .7 0 .0哎︺心JO护2‘U ..…,几1几月峥︸6万一一一一一q︺2﹃f甘月J只U2. 4. 7. 3.1.一一一一一72内J Zn甘2. 3. 7. 3.L一一一一一 一,孟勺白飞甘,曰,上0113001003020354081801520015030804280826似30U00450354U0500U0翻ID一一3.2, 2.7一一1.8, 0.7一一7.8, 10.0一一4 .9,王4.9一 4 .50323似580…     

I.低频甚低频传播突然扰动

上J,8年 了日 {J 开始START (UT)极大MAX(UT)结束END(UT)级别IMPSPALF合甲(拜s)△,。(邵) SPA VLF△甲(户s) SFA LF△A(dB)I.低频甚低频传播突然扰动~~     

I.低频甚低频传播突然扰动

洲IMP掀END(UT)公犯2年 11月 日 开始SrART(Ur)SPA1万班叭班认VIJI万仰(娜)勿〕(娜)△和(娜)△A(dB)01乃0213014102190612伪120337 一4 .2 一1 .2 一4 .5一2 .1,+0.9 一1 .3OU恤J7矛0护b2‘.二月J心JC︸︸一一一一2 nU‘J 00哎甘2心12内J︵U 一一一︸一+一+一‘.几‘.几内乙内‘‘几.,二月.﹃一一2.3,+1.9内J 4 401几4 Zn匕 一一一一心几n,O口护心心」弓︸几U .1‘.几7 一一一一一7气即7月JZ月J nU‘l‘1咤砂 一一一一一+一内‘11口.L‘.二内」0抖30135优拼3D优纷5价加D价叨例加价05价阅03(扣U以07015ZD内J弓J 2 244 72…     

I.低频甚低频传播突然扰动

1996年 4月 日 少Q 开始START (UT) 0225 0302 0334极大MAX(UT)023903070342结束END(UT)0300D033OD0420D级别IMP SPA LF△甲(件s)△甲。(拜s)一2,7一2 .8一1 .7一1.8一3 .9一4.1 SPA VLF△甲(拼s)1十1Q SFA LF △A(dB) 一6 .5 一1 .8一1 .5,丰2.8夕曰少‘口﹄Q︺I.低频甚低频传播突然扰动~~     

I.低频甚低频传播突然扰动

加似年 U月 日 开始Sr八Rr结束级别ENDI侧[P汾叭廿牙叭班叭VLF】万(UT)(UT)仰(脚)匆,(脾)鲡,(件)△A(dB)︸吕八U血U7︵吕决“︸2︵吕内J内」 一一︸一︸8 7 SE 5E9nU‘.1叮曰O夕4一一一一一廿02‘11 22自U口.几2,自傀曰 一一一一一035301邪,二2例肠0201仪扮509100137住甘矛O ,孟7 OJR︸2 OJ︸“︸2八U 20夕,创n︸ 一︸++一-7 8 6 66E自U八U nU‘.几一O一一一一一心口JO 4 70nU nU丹U八UZ 一︸一一一0331朋肠0452价160816一0 .9一1 .5一0 .410 101010101092E压80八U舟,﹄尸02‘.1一一一一一弓洲】1佣16侧巧201仍0217一0 .…     

I.低频甚低频传播突然扰动

2以左年3月日 开始51’A RT(UT)驴A1万班伙班叭VLFI万仰(牌)鲡(牌)鲡(娜)△A(dB)划IMP棘END(UT)74夕0 007.且‘且4 4 11十一一一一,二71乃护0 .17八11︸22‘.几一︸一一一月J︵吕一U,1 nU月呀nUZ内‘,几一一一一一 一十+内J‘.二,几,且‘且nUO夕2,12,几︵“︸.几,几2一一一一一7 J67咤甘R︸nU‘.工C甘n甘n甘 一一一一一心JO夕护0 42nU nUC甘n甘,几一一一一一一︸一一‘.二月几‘.几,几吸二伙刃7价31加130乞场05洲021103加0611价漪035504540333以抖5仪巧OU肠210之扣0320肠肠价只0415U05160355U护0 lj QO月峥,孟nU﹄U nU民…     

I.低频甚低频传播突然扰动

1995年 10月 日 开始51,ART (UT)级别U以PSPALFSPAVLF仰(件)却(邵)却(仰)‘SFA LF仓A(dB)目仪界故津,本月无数据。I.低频甚低频传播突然扰动~~     

天文教育I: 万有引力与天体物理

分别从物理学和天文学角度引申出天体物理学科, 特别关注万有引力在其中扮演的关键角色. 无论在综合性大学亦或理工科院校, 天文教育均有益于提高学生的科学和人文素养, 而天体物理则是天文学的主要内涵. 介绍了作者讲授``天体物理''课程的相关信息以及个人认识. 最后, 以大气簇射mu子产生、啾质量、宇宙加速膨胀等教学案例结束, 侧面诠释了作者的``天体物理''教育理念.