前報では,保持器振れに対する玉配置の影響を理論的に解析した.本報では,直径の異なる玉を適宜配置させて,保持器振れの測定を行った.軸受としての玉径相互差は同じであっても,寸法差を与えた玉の配置によって,保持器振れは大きく異なっており,前報の理論解析の妥当性を確認できた.

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Generally speaking, a rotating spindle is supported by at least two rolling bearings. Though the fixing error of the rolling bearing is strictly controlled, it can’t be zero due to the form errors of the elements of a rolling bearing, the difference of dynamic accuracy for the individual rolling bearing, and so on. Therefore, in manufacturing process of a spindle, the rotating accuracy of the spindle is measured with changing the fixing phase of the rolling bearing which supports the spindle. In this process, human intuition and experience have a very important role. When the run-out of the rotating spindle becomes minimum, the attitude of the rolling bearings is fixed. In such a practical technique, the spindle is assembled. In this research, the practical technique, which is not reported in the past, is studied. Consequently, the influence of the fixing phase and the inclination error of the rolling bearing to the non-repetitive run-out (NRRO) of the spindle was clarified quantitatively.

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This paper deals with the behavior of the balls that exist between the grooves of the hypotrochoid plate and the epitrochoid plate in a standard ball reducer. As a first step to elucidate the behavior of balls in a standard ball reducer, we measured and analyzed the ball center locus, the ball passage period, and the ball orbital period. From the results of measurements and analyses, the conclusions were obtained as follow: (1) The ball center locus is hypotrochoid, which is fixed on a coordinate system at rest. The wave number of the ball center locus is equal to that of the groove of the hypotrochoid plate. (2) The ball passage period is equal to the rotational period of the input shaft. (3) The ball orbital period is the product of the rotational period of the input shaft and number of the halls.

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太陽系（Solar System）における太陽の自転と惑星の公転に関する共鳴関係、並びに、惑星の自転と衛星の公転に関する共鳴関係、等のフラクタル構造について、数理モデル（Virtual Hula-HoopMathematical Model）を提案する。 次に、共鳴関係を長構造的に音楽情報にマッピングして協和音（Concord）の存在を検証する。 更に、逆問題としてのこの数理モデルを物理モデルに結び付ける為の、重力の情報システムについて考察する。

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太陽系（Solar System）における 太陽の自転と惑星の公転に関する共鳴関係，並びに，惑星の自転と衛星の公転 に関する共鳴関係，等のフラクタル構造について，数理モデル（Virtual Hula-Hoop Mathematical Model）を提案する。 次に，共鳴関係を長構造的に音楽情報にマッピングして協和音（Concord）の存在を検証する。 更に，逆問題としてのこの数理モデルを物理モデルに結び付ける為の，重力の情報システムについて考察する。

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現代物理のキーワード

古在–Lidov機構とその最近の進展

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Generally, rolling bearings are fixed at both ends of a rotating axis and a reference target is provided to give allowable fixing error of the bearings as appropriate according to the category and application. The allowable fixing error of a spindle, in which high rotational accuracy is required, should be very small. However, there is no research report which investigates closely the relationship between the fixing error and the rotational accuracy. Thus, eventually, this research intends to clarify the relationship between them and this report describes the relationship between the inclination error in bearing unit and the non-repetitive run-out using small ball rolling bearing. Consequently, using a measuring equipment of rotational error for single ball bearing, it was made known that the amplitude of the ball-cage rotation becomes very large when the inclination error increases. Thus, the conclusions of this research are as follows. (1) When the inclination error increases, the amplitude of frequency of cage rotation becomes large even supposing that the inclination error is in an allowable range. (2) When the inclination error increases, the amplitude of the doubled frequency of cage rotation becomes prominent. (3) When the number of rolling elements becomes large, the increment of variation of rotational period for the ball-cage is small.

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木星の衛星食による光速度測定は食の固有周期を高い粘度で求めることが必要なため,眼視観測によってはほとんど不可能である。ビデオカメラによる食の撮影・記録とコンピューターを使った解析によって食時刻の測定精度を飛躍的に高めることができ光速度の導出が可能になる。2000年の観測結果とあわせてこの問題に対する我々の理解の進展を報告する。

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ボールねじを用いた送り系では，ねじ軸回転角とナット移動量の間に非線形的な関係が生じる．この現象は「ロストモーション」と呼ばれ，精密位置決めを行う際に位置決め誤差の原因となることが知られている．本研究では，ボールねじの軌道ねじれによる玉の食い込み・すべり挙動に起因する玉の公転運動の遅れが，ボールねじに生じるロストモーションの発生とどのような関係があるのか調べている．

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As is well known, the famous research of Ore C. Romer, who has confirmed the finiteness of light velocity and has estimated the value of it, is a very remarkable and important work in the history of physics. However, as is seen in several articles, it seems that there have been distributed rather widely some incomplete or erroneous understandings concerning his work. In this short note, studies are made on the investigating process of Romer on the problems of velocity of light, including some remarks of the interpretation of it in modern mathematical words.

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人工衛星は万有引力の法則が太陽系の惑星以外の物体の運動にも適用できることを示す教材になる。アマチュア衛星のビーコンを受信すれば衛星の可視時間を測定できる。可視時間から衛星のや速さを求めて理論値と比較すれば,ケプラーの第3法則や万有引力の法則を検証することができる。人工衛星の軌道要素として公表されている数値データを利用すれば,さらに精度の高い検証が可能である。

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High carbon chromium bearing steel (SUJ2) is generally used for the rolling element of ball bearing as its material. Normal form of the bearing steel is wire rod. Then rough spheres are made by forging and they are developed gradually into high accurate rolling elements by heat treatment and polishing. However, it is known heretofore that there is inhomogeneous stress distribution caused by forging and heat treatment inside the rolling element. Recently, usage environment of rolling bearings tightens, in other words, high-speed and high temperature conditions are increasingly applied. Though increasing the environmental temperature is well-known as a stress releasing technique for metal stock, moderate deformation arises in the material. When such stress releasing inside the rolling element is enforced at work with being heated to a high temperature, the geometrical form error of rolling element enlarge and the bearing performance will decay. Therefore in this research, relating to the bearing steel ball and silicon nitride ball, the relationship between the non-repetitive run-out (NRRO) of the bearing and the changes in dimensional and geometrical form (roundness) of the rolling element which is exposed to high temperature for one year, assuming its use in a hot environment, are described. As a result, the followings were clarified. (1) For SUJ2 ball, high temperature environment enforced the change of not only geometrical form error but also diameter insomuch as differing accuracy grade. This causes the deterioration of bearing performance. (2) For silicon nitride (Si₃N₄) ball, under the same condition, the changes of geometrical form error and diameter are very few. Then, the authors confirmed that the silicon nitride ball has a beneficial effect on the usage in a hot environment.

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本研究は，中学生の「月の満ち欠け」におけるつまずきを習熟度別に明らかにし，「月の満ち欠け」の学習に必要な知識・技能を身に付けさせるための学習指導法を検討することを目的に行った．4種類の問題(A問題，B問題，C問題，D問題)を解かせ，答案の分析を行った．その結果，中学生を5グループに分類でき，それぞれのグループ間において何の知識・技能が習得できずにつまずいているのかが明らかになった．そして，それらの知識・技能を総括すると，中学生を指導するには，特に「月の

とその公転方向を指摘できる能力」「太陽の位置から観察時刻を推定できる能力」「地球の自転に合わせて南向きに立つ観察者を含む地平線（左手が東，中央が南，右手が西）を回転させられる能力」に重点を置いて指導していくことの必要性が明らかになった．

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