[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/115317#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/115317","headline":"\u89d2\u904b\u52d5\u91cf – Wikipedia","name":"\u89d2\u904b\u52d5\u91cf – Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u89d2\u904b\u52d5\u91cf”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082011\u5e7410\u6708\uff09 \u89d2\u904b\u52d5\u91cf\uff08\u304b\u304f\u3046\u3093\u3069\u3046\u308a\u3087\u3046\u3001\u82f1\u8a9e: angular momentum\uff09\u3068\u306f\u3001\u904b\u52d5\u91cf\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u8868\u3059\u529b\u5b66\u306e\u6982\u5ff5\u3067\u3042\u308b\u3002 \u4f4d\u7f6e r \u306b\u304a\u3044\u3066\u3001\u904b\u52d5\u91cf p \u3092\u6301\u3064\u8cea\u70b9\u306e\u539f\u70b9\u307e\u308f\u308a\u306e\u89d2\u904b\u52d5\u91cf L \u306f L\u2261r\u00d7p{displaystyle","datePublished":"2022-03-18","dateModified":"2022-03-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/115317","about":["Wiki"],"wordCount":9721,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u89d2\u904b\u52d5\u91cf”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082011\u5e7410\u6708\uff09\u89d2\u904b\u52d5\u91cf\uff08\u304b\u304f\u3046\u3093\u3069\u3046\u308a\u3087\u3046\u3001\u82f1\u8a9e: angular momentum\uff09\u3068\u306f\u3001\u904b\u52d5\u91cf\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u8868\u3059\u529b\u5b66\u306e\u6982\u5ff5\u3067\u3042\u308b\u3002\u4f4d\u7f6e r \u306b\u304a\u3044\u3066\u3001\u904b\u52d5\u91cf p \u3092\u6301\u3064\u8cea\u70b9\u306e\u539f\u70b9\u307e\u308f\u308a\u306e\u89d2\u904b\u52d5\u91cf L \u306fL\u2261r\u00d7p{displaystyle {boldsymbol {L}}equiv {boldsymbol {r}}times {boldsymbol {p}}}\u3067\u5b9a\u7fa9\u3055\u308c\u308b[\u6ce8\u91c8 1]\u3002\u3053\u3053\u3067\u3001\u00d7 \u306f\u5916\u7a4d\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\u3001\u89d2\u904b\u52d5\u91cf\u306e\u5927\u304d\u3055 L \u306fL=rpsin\u2061\u03b8{displaystyle L=rp,sin theta }\u3068\u8868\u3055\u308c\u308b\u3002\u3053\u3053\u3067\u3001\u03b8 \u306f r \u3068 p \u306e\u306a\u3059\u89d2\u3092\u3001r, p \u306f\u305d\u308c\u305e\u308c r, p \u306e\u5927\u304d\u3055\u3092\u8868\u3059\u3002\u8cea\u70b9\u304c\u8cea\u91cf m\u3001\u901f\u5ea6 v \u306e\u3068\u304d\u3001\u904b\u52d5\u91cf\u306f p = mv \u3067\u3042\u308a\u3001\u89d2\u904b\u52d5\u91cf\u306fL=r\u00d7mv=mr\u00d7v{displaystyle {boldsymbol {L}}={boldsymbol {r}}times m{boldsymbol {v}}=m{boldsymbol {r}}times {boldsymbol {v}}}\u3068\u306a\u308b\u3002\u307e\u305f\u3001\u89d2\u901f\u5ea6\u304c \u03c9 \u306e\u3068\u304d\u3001\u89d2\u904b\u52d5\u91cf\u306fL=I\u03c9{displaystyle {boldsymbol {L}}=I{boldsymbol {omega }}}\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u3053\u3067 I \u306f\u6163\u6027\u30c6\u30f3\u30bd\u30eb\u3067\u3042\u308b\u3002Table of Contents\u5ea7\u6a19\u539f\u70b9\u306e\u79fb\u52d5[\u7de8\u96c6]\u904b\u52d5\u65b9\u7a0b\u5f0f[\u7de8\u96c6]\u89d2\u904b\u52d5\u91cf\u306e\u4fdd\u5b58[\u7de8\u96c6]\u8cea\u70b9\u7cfb\u306e\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u56de\u8ee2\u904b\u52d5\u3068\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u89d2\u901f\u5ea6[\u7de8\u96c6]\u91cf\u5b50\u529b\u5b66\u3067\u306e\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u3067\u306e\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u5bfe\u79f0\u6027\u3068\u306e\u95a2\u4fc2[\u7de8\u96c6]\u6ce8\u91c8[\u7de8\u96c6]\u51fa\u5178[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u5ea7\u6a19\u539f\u70b9\u306e\u79fb\u52d5[\u7de8\u96c6]\u89d2\u904b\u52d5\u91cf\u306f\u3001\u305d\u306e\u5b9a\u7fa9\u304b\u3089\u5ea7\u6a19\u539f\u70b9\u306e\u9078\u629e\u306b\u4f9d\u5b58\u3059\u308b\u3002\u539f\u70b9\u3092\u4f4d\u7f6e a \u3078\u79fb\u52d5\u3057\u305f\u5ea7\u6a19\u7cfb\u3092\u8003\u3048\u308b\u3002\u65b0\u305f\u306a\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b\u91cf\u3092 ‘ \u3092\u4ed8\u3051\u3066\u8868\u3059\u3082\u306e\u3068\u3059\u308c\u3070\u3001r‘ = r \u2212 a, p‘ = p \u3067\u3042\u308a  L\u2032=r\u2032\u00d7p\u2032=r\u00d7p\u2212a\u00d7p=L\u2212a\u00d7p{displaystyle {boldsymbol {L}}’={boldsymbol {r}}’times {boldsymbol {p}}’={boldsymbol {r}}times {boldsymbol {p}}-{boldsymbol {a}}times {boldsymbol {p}}={boldsymbol {L}}-{boldsymbol {a}}times {boldsymbol {p}}}\u3068\u306a\u308b.\u904b\u52d5\u65b9\u7a0b\u5f0f[\u7de8\u96c6]\u8cea\u70b9\u306e\u89d2\u904b\u52d5\u91cf\u306e\u6642\u9593\u5909\u5316\u306f  dLdt=r\u00d7dpdt+drdt\u00d7p{displaystyle {frac {d{boldsymbol {L}}}{dt}}={boldsymbol {r}}times {frac {d{boldsymbol {p}}}{dt}}+{frac {d{boldsymbol {r}}}{dt}}times {boldsymbol {p}}}\u3068\u306a\u308b\u3002\u3053\u3053\u3067\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f dp\/dt = F \u3092\u7528\u3044\u308c\u3070\u3001\u7b2c\u4e00\u9805\u306f\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8 N = r\u00d7F \u3068\u306a\u308b\u3002\u307e\u305f\u3001\u7b2c\u4e8c\u9805\u306f (dr\/dt)\u00d7p = mv\u00d7v = 0 \u3068\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u89d2\u904b\u52d5\u91cf\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3068\u540c\u69d8\u306a\u30aa\u30a4\u30e9\u30fc\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f  dLdt=N{displaystyle {frac {d{boldsymbol {L}}}{dt}}={boldsymbol {N}}}\u3092\u6e80\u305f\u3059\u3002\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306f\u305d\u306e\u5b9a\u7fa9\u304b\u3089\u5ea7\u6a19\u539f\u70b9\u306e\u9078\u629e\u306b\u4f9d\u5b58\u3059\u308b\u3002\u3057\u304b\u3057\u3001\u5ea7\u6a19\u539f\u70b9\u306e\u79fb\u52d5\u306b\u3088\u308b\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u5909\u5316\u3068\u89d2\u904b\u52d5\u91cf\u306e\u5909\u5316\u304c\u76f8\u6bba\u3055\u308c\u3001\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u5e38\u306b\u6210\u308a\u7acb\u3064\u3002\u89d2\u904b\u52d5\u91cf\u306e\u4fdd\u5b58[\u7de8\u96c6]\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u304c 0 \u3067\u3042\u308b\u3068\u304d\u3001\u89d2\u904b\u52d5\u91cf\u306f\u6642\u9593\u3068\u3068\u3082\u306b\u5909\u5316\u305b\u305a\u4e00\u5b9a\u3068\u306a\u308b\u3002\u3053\u306e\u3053\u3068\u3092\u89d2\u904b\u52d5\u91cf\u4fdd\u5b58\u306e\u6cd5\u5247\uff08\u89d2\u904b\u52d5\u91cf\u306e\u4fdd\u5b58\u5247\uff09\u3068\u3044\u3046\u3002\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u304c 0 \u3068\u306a\u308b\u306e\u306f\u3001\u529b\u304c 0 \u3067\u3042\u308b\u304b\u3001\u529b\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u5e73\u884c\u3067\u3042\u308b\u3068\u304d\u3067\u3042\u308b\u3002\u529b\u304c\u4f5c\u7528\u3057\u3066\u3044\u306a\u3044\u3068\u304d\u306f\u7b49\u901f\u76f4\u7dda\u904b\u52d5\u3068\u306a\u308b\u3002\u7b49\u901f\u76f4\u7dda\u904b\u52d5\u306b\u304a\u3044\u3066\u306f\u904b\u52d5\u91cf\u3068\u89d2\u904b\u52d5\u91cf\u306f\u3068\u3082\u306b\u4fdd\u5b58\u3059\u308b\u3002\u3053\u308c\u306b\u5bfe\u3057\u7b49\u901f\u5186\u904b\u52d5\u306b\u304a\u3044\u3066\u306f\u3001\u904b\u52d5\u91cf\u306e\u5927\u304d\u3055\u306f\u4e00\u5b9a\u3067\u3042\u308b\u304c\u5411\u304d\u304c\u6642\u9593\u306b\u3088\u308a\u5909\u5316\u3059\u308b\u305f\u3081\u904b\u52d5\u91cf\u306f\u4fdd\u5b58\u305b\u305a\u3001\u89d2\u904b\u52d5\u91cf\u306e\u307f\u304c\u4fdd\u5b58\u3059\u308b\u3002\u529b\u304c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3068\u5e73\u884c\u3067\u3042\u308b\u3068\u304d\u306fF(r)=f(r)r{displaystyle {boldsymbol {F}}({boldsymbol {r}})=f(r),{boldsymbol {r}}}\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u5f62\u306e\u529b\u306f\u4e2d\u5fc3\u529b\u3068\u547c\u3070\u308c\u308b\u3002\u8cea\u70b9\u7cfb\u306e\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u89d2\u904b\u52d5\u91cf\u306f\u52a0\u6cd5\u7684\u306a\u91cf\u3067\u3042\u308a\u3001\u7cfb\u306e\u5168\u89d2\u904b\u52d5\u91cf\u306f\u3001\u90e8\u5206\u306e\u89d2\u904b\u52d5\u91cf\u306e\u548c\u3067\u3042\u3089\u308f\u3055\u308c\u308b\u3002\u8cea\u70b9\u7cfb\u306e\u5168\u89d2\u904b\u52d5\u91cf L \u306f\u3001\u8cea\u70b9 i \u306e\u89d2\u904b\u52d5\u91cf\u3092 li \u3068\u3059\u308c\u3070L=\u2211ili=\u2211iri\u00d7pi{displaystyle {boldsymbol {L}}=sum _{i}{boldsymbol {l}}_{i}=sum _{i}{boldsymbol {r}}_{i}times {boldsymbol {p}}_{i}}\u3067\u3042\u308b\u3002\u8cea\u91cf\u4e2d\u5fc3 rg \u306b\u5168\u8cea\u91cf M \u304c\u3042\u308b\u3068\u8003\u3048\u305f\u3068\u304d\u306e\u89d2\u904b\u52d5\u91cf\u306fLg=Mrg\u00d7drgdt{displaystyle {boldsymbol {L}}_{mathrm {g} }=M{boldsymbol {r}}_{mathrm {g} }times {frac {d{boldsymbol {r}}_{mathrm {g} }}{dt}}}\u3068\u306a\u308b\u3002\u5168\u89d2\u904b\u52d5\u91cf\u3068 Lg \u306e\u5dee\u306f\u3001\u8cea\u91cf\u4e2d\u5fc3\u304b\u3089\u307f\u305f\u76f8\u5bfe\u904b\u52d5\u306e\u89d2\u904b\u52d5\u91cf\u3068\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002Lr=L\u2212Lg{displaystyle {boldsymbol {L}}_{mathrm {r} }={boldsymbol {L}}-{boldsymbol {L}}_{mathrm {g} }}\u8cea\u70b9 i \u306e\u89d2\u904b\u52d5\u91cf\u306e\u6642\u9593\u5909\u5316\u306f\u3001\u8cea\u70b9 i \u306b\u4f5c\u7528\u3059\u308b\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8 Ni = ri\u00d7Fi \u306b\u7b49\u3057\u304fdlidt=Ni=ri\u00d7Fi{displaystyle {frac {d{boldsymbol {l}}_{i}}{dt}}={boldsymbol {N}}_{i}={boldsymbol {r}}_{i}times {boldsymbol {F}}_{i}}\u3092\u6e80\u305f\u3059\u3002\u3053\u3053\u3067\u8cea\u70b9 i \u306b\u4f5c\u7528\u3059\u308b\u529b Fi \u3092\u3001\u5916\u529b fi \u3068\u3001\u8cea\u70b9 j \u304c\u53ca\u307c\u3059\u5185\u90e8\u76f8\u4e92\u4f5c\u7528 fij \u306b\u5206\u308b\u3068\u3001\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306fNi=ri\u00d7(fi+\u2211jfij){displaystyle {boldsymbol {N}}_{i}={boldsymbol {r}}_{i}times ({boldsymbol {f}}_{i}+sum _{j}{boldsymbol {f}}_{ij})}\u3068\u8868\u3055\u308c\u308b\u3002\u5168\u89d2\u904b\u52d5\u91cf\u306e\u6642\u9593\u5909\u5316\u3092\u8003\u3048\u308b\u3068dLdt=\u2211idlidt=\u2211iri\u00d7fi+\u2211i,jri\u00d7fij{displaystyle {frac {d{boldsymbol {L}}}{dt}}=sum _{i}{frac {d{boldsymbol {l}}_{i}}{dt}}=sum _{i}{boldsymbol {r}}_{i}times {boldsymbol {f}}_{i}+sum _{i,j}{boldsymbol {r}}_{i}times {boldsymbol {f}}_{ij}}\u3068\u306a\u308b\u3002\u904b\u52d5\u306e\u7b2c3\u6cd5\u5247\u304b\u3089 fji = \u2212fij \u306a\u306e\u3067\u3001\u5185\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u548c\u306f\u2211i,jri\u00d7fij=12\u2211i,j(ri\u00d7fij\u2212ri\u00d7fji)=12\u2211i,j(ri\u2212rj)\u00d7fij{displaystyle sum _{i,j}{boldsymbol {r}}_{i}times {boldsymbol {f}}_{ij}={frac {1}{2}}sum _{i,j}({boldsymbol {r}}_{i}times {boldsymbol {f}}_{ij}-{boldsymbol {r}}_{i}times {boldsymbol {f}}_{ji})={frac {1}{2}}sum _{i,j}({boldsymbol {r}}_{i}-{boldsymbol {r}}_{j})times {boldsymbol {f}}_{ij}}\u3068\u5909\u5f62\u3067\u304d\u308b\u3002\u3053\u3053\u3067\u3001\u5185\u529b\u304c\u4e2d\u5fc3\u529b\u3067\u3042\u308b\u306a\u3089\u3070\u3001\u5185\u529b fij \u306f\u8cea\u70b9 i \u306e\u8cea\u70b9 j \u304b\u3089\u898b\u305f\u76f8\u5bfe\u4f4d\u7f6e ri \u2212 rj \u3068\u5e73\u884c\u3067\u3001\u5185\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u548c\u306f 0 \u3068\u306a\u308b\u3002\u3053\u306e\u3068\u304ddLdt=\u2211iri\u00d7fi{displaystyle {frac {d{boldsymbol {L}}}{dt}}=sum _{i}{boldsymbol {r}}_{i}times {boldsymbol {f}}_{i}}\u3068\u306a\u308a\u3001\u8cea\u70b9\u7cfb\u306e\u5168\u89d2\u904b\u52d5\u91cf\u306e\u6642\u9593\u5909\u5316\u306f\u4f5c\u7528\u3059\u308b\u5916\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u7dcf\u548c\u3068\u7b49\u3057\u304f\u306a\u308b\u3002\u56de\u8ee2\u904b\u52d5\u3068\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]  \u56fa\u5b9a\u3055\u308c\u305f\u56de\u8ee2\u8ef8\u3092\u3082\u3064\u7cfb\u306b\u5bfe\u3057\u3066\u3001\u529b\u3092\u4f5c\u7528\u3055\u305b\u305f\u6642\u306e\u7269\u7406\u91cf\u306e\u95a2\u4fc2\u3002\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8 \u03c4 \u3068\u3001\u4f4d\u7f6e r \u3068\u529b F \u3068\u306e\u95a2\u4fc2\uff08\u4e0a\u306e\u5f0f\uff09\u3001\u304a\u3088\u3073\u89d2\u904b\u52d5\u91cf L \u3068\u4f4d\u7f6e r \u3068\u904b\u52d5\u91cf p \u3068\u306e\u95a2\u4fc2\uff08\u4e0b\u306e\u5f0f\uff09\u3002\u89d2\u904b\u52d5\u91cf\u306f\u56de\u8ee2\u904b\u52d5\u3068\u6df1\u304f\u95a2\u4fc2\u3057\u3066\u3044\u308b\u7269\u7406\u91cf\u3067\u3042\u308b\u3002\u305f\u3060\u3057\u3001\u89d2\u904b\u52d5\u91cf\u81ea\u4f53\u306f\u56de\u8ee2\u904b\u52d5\u3092\u3057\u3066\u3044\u306a\u304f\u3068\u3082\u5b9a\u7fa9\u3055\u308c\u308b\u7269\u7406\u91cf\u3067\u3042\u308b\u3002\u60d1\u661f\u9593\u306b\u50cd\u304f\u4e07\u6709\u5f15\u529b\u306f\u4e2d\u5fc3\u529b\u3067\u3042\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u3001\u60d1\u661f\u306e\u89d2\u904b\u52d5\u91cf\u306f\u4fdd\u5b58\u3055\u308c\u308b\u3002\u4fdd\u5b58\u5247\u306f\u3001\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c2\u6cd5\u5247\u306e\u300c\u9762\u7a4d\u901f\u5ea6\u4e00\u5b9a\u300d\u3068\u5bc6\u63a5\u306a\u95a2\u308f\u308a\u304c\u3042\u308b\u3002\u6642\u523b t \u306b\u304a\u3051\u308b\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb r(t) \u3068\u3001\u5fae\u5c0f\u306a\u6642\u9593 dt \u304c\u7d4c\u3063\u305f\u5f8c\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb r(t + dt) \u304c\u4f5c\u308b\u5fae\u5c0f\u306a\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u306fdS=12r(t)\u00d7r(t+dt){displaystyle d{boldsymbol {S}}={frac {1}{2}}{boldsymbol {r}}(t)times {boldsymbol {r}}(t+dt)}\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\u3001\u9762\u7a4d\u901f\u5ea6\u306fdSdt=12r(t)\u00d7v(t)=12mL(t){displaystyle {frac {d{boldsymbol {S}}}{dt}}={frac {1}{2}}{boldsymbol {r}}(t)times {boldsymbol {v}}(t)={frac {1}{2m}}{boldsymbol {L}}(t)}\u3068\u306a\u308a\u3001\u9762\u7a4d\u901f\u5ea6\u304c\u4e00\u5b9a\u306a\u3089\u3070\u3001\u89d2\u904b\u52d5\u91cf\u3082\u4e00\u5b9a\u3068\u306a\u308b\u3002\u89d2\u901f\u5ea6[\u7de8\u96c6]\u89d2\u901f\u5ea6 \u03c9 \u306f\u03c9=2r2dSdt=1r2r\u00d7v{displaystyle {boldsymbol {omega }}={frac {2}{r^{2}}}{frac {d{boldsymbol {S}}}{dt}}={frac {1}{r^{2}}}{boldsymbol {r}}times {boldsymbol {v}}}\u3068\u8868\u3055\u308c\u308b\u3002\u5f93\u3063\u3066\u3001\u8cea\u70b9\u306e\u6163\u6027\u30e2\u30fc\u30e1\u30f3\u30c8\u306fI=mr2{displaystyle I=mr^{2}}\u3068\u306a\u308b\u3002\u539f\u70b9\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u5186\u904b\u52d5\u3092\u3057\u3066\u3044\u308b\u8cea\u70b9\u306e\u901f\u5ea6 v \u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3002v=\u03c9\u00d7r{displaystyle {boldsymbol {v}}={boldsymbol {omega }}times {boldsymbol {r}}}\u91cf\u5b50\u529b\u5b66\u3067\u306e\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u91cf\u5b50\u529b\u5b66\u3067\u306f\u3001\u89d2\u904b\u52d5\u91cf\u306f\u4ee5\u4e0b\u306e\u4ea4\u63db\u95a2\u4fc2\u3092\u6e80\u305f\u3059\u6f14\u7b97\u5b50 J^{displaystyle {hat {boldsymbol {J}}}} \u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002[J^x,J^y]=iJ^z,\u00a0[J^y,J^z]=iJ^x,\u00a0[J^z,J^x]=iJ^y{displaystyle [{hat {J}}_{x},{hat {J}}_{y}]=i{hat {J}}_{z},~[{hat {J}}_{y},{hat {J}}_{z}]=i{hat {J}}_{x},~[{hat {J}}_{z},{hat {J}}_{x}]=i{hat {J}}_{y}}\u3042\u308b\u3044\u306f\u30013\u3064\u306e\u5f0f\u3092\u307e\u3068\u3081\u3066[J^i,J^j]=i\u03f5ijkJ^k{displaystyle [{hat {J}}_{i},{hat {J}}_{j}]=iepsilon _{ijk}{hat {J}}_{k}}\u03f5ijk{displaystyle epsilon _{ijk}} \u306f\u5b8c\u5168\u53cd\u5bfe\u79f0\u30c6\u30f3\u30bd\u30eb\u3067\u3042\u308b\u3002\u3053\u308c\u3089\u306e\u4ea4\u63db\u95a2\u4fc2\u306f\u89d2\u904b\u52d5\u91cf\u4ee3\u6570\u3068\u547c\u3070\u308c\u308b\u3002\u3053\u306e\u89d2\u904b\u52d5\u91cf\u306e\u6027\u8cea\u3092\u8abf\u3079\u308b\u3068\u3001J^=L^+S^{displaystyle {hat {boldsymbol {J}}}={hat {boldsymbol {L}}}+{hat {boldsymbol {S}}}}\u306e\u4e8c\u3064\u306e\u90e8\u5206\u306b\u5206\u3051\u3089\u308c\u3001\u305d\u308c\u305e\u308c\u304c\u89d2\u904b\u52d5\u91cf\u4ee3\u6570\u3092\u6e80\u305f\u3059\u3002[L^i,L^j]=i\u03f5ijkL^k,\u00a0[S^i,S^j]=i\u03f5ijkS^k,\u00a0[L^i,S^j]=0{displaystyle [{hat {L}}_{i},{hat {L}}_{j}]=iepsilon _{ijk}{hat {L}}_{k},~[{hat {S}}_{i},{hat {S}}_{j}]=iepsilon _{ijk}{hat {S}}_{k},~[{hat {L}}_{i},{hat {S}}_{j}]=0}\u8ecc\u9053\u89d2\u904b\u52d5\u91cf L^{displaystyle {hat {boldsymbol {L}}}} \u306f\u3001 L^=r^\u00d7p^{displaystyle {hat {boldsymbol {L}}}={hat {boldsymbol {r}}}times {hat {boldsymbol {p}}}} \u306e\u3088\u3046\u306b\u4f4d\u7f6e\u3068\u904b\u52d5\u91cf\u306e\u5916\u7a4d\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u56fa\u6709\u5024\u304c\u6574\u6570\u306e\u307f\u306b\u9650\u3089\u308c\u308b\u3002\u30b9\u30d4\u30f3\u89d2\u904b\u52d5\u91cf S^{displaystyle {hat {boldsymbol {S}}}} \u306f\u3001\u4f4d\u7f6e\u3068\u904b\u52d5\u91cf\u3067\u306f\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305a\u3001\u305d\u306e\u56fa\u6709\u5024\u304c\u6574\u6570\u306b\u52a0\u3048\u3066\u534a\u6574\u6570\u3082\u8a31\u3055\u308c\u308b\u3002\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u3067\u306e\u89d2\u904b\u52d5\u91cf[\u7de8\u96c6]\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u306b\u304a\u3044\u3066\u306f\u4e8c\u968e\u30c6\u30f3\u30bd\u30ebL\u03bc\u03bd{displaystyle L^{mu nu }}\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\tL\u03bc\u03bd=2!x[\u03bcp\u03bd]\u2192[0Lz\u2212LycNx\u2212Lz0LxcNyLy\u2212Lx0cNz\u2212cNx\u2212cNz\u2212cNy0]{displaystyle L^{mu nu }=2!x^{[mu }p^{nu ]}rightarrow {begin{bmatrix}0&L^{z}&-L^{y}&cN^{x}\\-L^{z}&0&L^{x}&cN^{y}\\L^{y}&-L^{x}&0&cN^{z}\\-cN^{x}&-cN^{z}&-cN^{y}&0\\end{bmatrix}}}\u3053\u3053\u3067\uff0c\u56db\u5143\u4f4d\u7f6ex\u03bc{displaystyle x^{mu }}\uff0c\u56db\u5143\u904b\u52d5\u91cfp\u03bc{displaystyle p^{mu }}\uff0c\u304a\u3088\u3073\u8cea\u91cf\u30e2\u30fc\u30e1\u30f3\u30c8N{displaystyle {boldsymbol {N}}}\u306f\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u3002(x\u03bc)=(x,\u00a0y,\u00a0z,\u00a0ct),(p\u03bc)=(px,\u00a0py,\u00a0pz,\u00a0E\/c),N=m(r\u2212vt){displaystyle {begin{aligned}(x^{mu })&=(x,~y,~z,~ct),\\(p^{mu })&=(p_{x},~p_{y},~p_{z},~E\/c),\\{boldsymbol {N}}&=m({boldsymbol {r}}-{boldsymbol {v}}t)end{aligned}}}\u5bfe\u79f0\u6027\u3068\u306e\u95a2\u4fc2[\u7de8\u96c6]\u89d2\u904b\u52d5\u91cf\u306f\u7a7a\u9593\u306e\u7b49\u65b9\u6027\uff08\u56de\u8ee2\u5bfe\u79f0\u6027\uff09\u306b\u5bfe\u5fdc\u3059\u308b\u4fdd\u5b58\u91cf\u3067\u3042\u308b\u3002\u7a7a\u9593\u306e\u4e00\u69d8\u6027\uff08\u4f75\u9032\u5bfe\u79f0\u6027\uff09\u306b\u5bfe\u5fdc\u3059\u308b\u4fdd\u5b58\u91cf\u3067\u3042\u308b\u904b\u52d5\u91cf\u3001\u6642\u9593\u306e\u4e00\u69d8\u6027\u306b\u5bfe\u5fdc\u3059\u308b\u4fdd\u5b58\u91cf\u3067\u3042\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u3068\u3082\u306b\u3001\u57fa\u672c\u7684\u306a\u7269\u7406\u91cf\u3067\u3042\u308b[1]\u3002\u305d\u308c\u305e\u308c\u300c\u89d2\u904b\u52d5\u91cf\u4fdd\u5b58\u306e\u6cd5\u5247\u300d\u3001\u300c\u904b\u52d5\u91cf\u4fdd\u5b58\u306e\u6cd5\u5247\u300d\u3001\u300c\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u306e\u6cd5\u5247\u300d\u306b\u95a2\u9023\u3065\u3051\u3089\u308c\u308b\u3002\u6ce8\u91c8[\u7de8\u96c6]^ \u901a\u5e38\u3001\u7c21\u5358\u306e\u305f\u3081\u306b\u56de\u8ee2\u4e2d\u5fc3\u3092\u539f\u70b9\u3068\u3059\u308b\u3002\u56de\u8ee2\u4e2d\u5fc3\u304c\u539f\u70b9\u3067\u306f\u306a\u304f\u70b9ro\u307e\u308f\u308a\u306e\u89d2\u904b\u52d5\u91cf\u3092\u6c42\u3081\u305f\u3044\u5834\u5408\u3001r\u3092\u76f8\u5bfe\u5ea7\u6a19r–ro\u306b\u7f6e\u304d\u63db\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u51fa\u5178[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/115317#breadcrumbitem","name":"\u89d2\u904b\u52d5\u91cf – Wikipedia"}}]}]