当前位置:首页>初中教材>初中物理课本背后的故事:科里奥利引进“功”与“动能”这两个物理术语

初中物理课本背后的故事:科里奥利引进“功”与“动能”这两个物理术语

  • 2026-03-29 18:43:57
初中物理课本背后的故事:科里奥利引进“功”与“动能”这两个物理术语

初中物理第十一章“功和机械能”(八年级下册)中,引进了功、动能和势能的概念。其中功与动能这两个名称,是由法国物理学家科里奥利提出来的。

科里奥利(Gaspard Gustave De Coriolis,1792-1843)出生于巴黎。他父亲曾是效忠法国国王路易十六的军官,在法国大革命后成了一名工业家。科里奥利16岁时,进入在拿破仑支持下建立的巴黎综合理工大学。他毕业时的成绩在同届学生中排名第二。

科里奥利24岁时,在巴黎综合理工大学的著名数学家柯西的推荐下,成为这所学校的数学教授。37岁时,他又在新成立的中央艺术与制造学院兼任力学教授。第二年(1830年),革命把查理十世赶下了台,柯西自愿跟随查理被流放,他的职位空了出来。大学请科里奥利接任柯西的职位。科里奥利这时经过十多年的积累,正进入科学创造时期,没有多余的时间和精力,拒绝了这个职位。不过,两年后,桥梁与道路学院的著名力学家纳维请科里奥利兼任自己助手,科里奥利接受了。4年后时,纳维去世,法兰西科学院推举科里奥利接替他做力学部的领头人。

科里奥利的身体一直不好。他同时兼任好几个职位,是很辛苦的。可是没有办法。自从父亲去世后,他必须承担起养活家人的责任(很可能由于身体不好,他没有考虑过结婚)

46岁时,科里奥利成了巴黎综合理工大学的教学主任,从此不必教学了,他在新岗位上干得非常出色。他甚至去关心学生学习的物质条件。他给教室安装的水冷器被大家称为“科里奥的水冷器”。

科里奥利的身体越来越差了。51岁时,他的生命结束了。他逝世前还在编辑一本书的书稿。这本书在他去世一年后出版。

许多科学家喜欢主张科学理论与技术应用完全分开。科里奥利不同意这种做法,认为理论应当与实际联系。他呼吁,要把力学理论用到对机器运行的分析上。正是基于对机器运动的分析,科里奥利在他37岁时出版的第一本著作中,赋予“功”这个词以专业含义,并提出“动能”这个词语。

古代的工匠在使用杠杆、滑轮组、轮盘等简单机械的长期经验中,发现了一个有趣的规律:每种机械运行时,在机械的这一头施加的力与受力部位移动距离的乘积,与机械的那一头提供的力与移动距离的乘积,常常近似相等。

这引起了人们对“力与距离的乘积”这个量的关注。后来的许多数学家和科学家,比如15世纪的达·芬奇,17世纪的莱布尼兹,都对“力与距离的乘积”给了很大注意。

科学家们用各种不同的名字称呼“力与距离的乘积”:什么机械动力啦,作用量啦,动力效率啦等等。情况一片混乱。

1821年(科里奥利29岁)时,法国著名物理学家与工程师库伦出版了一部著作。库伦在这部著作中考虑,人或动物在干活或工作时,需要克服一定的阻力;当人或动物干完一定的活后,就会精疲力尽,无法干更多的活(如果不补充食物的话)。看来,人或动物在干活时,需要消耗某种东西,而他(它)们身上储存的这种东西只有一定数量,一旦消耗完,就无法继续工作了。库伦试图找出一种方法,来定量描述人和动物能够完成的劳动量。

可能受到库伦著作的启发,科里奥利提出,用法语中的“工作”(travail)一词来称呼力与距离的乘积。人或动物或机器干完一定的活时,力与距离的乘积是多少,就说他(它)们做了多少“工作”(英文中表示工作的词是work。中文中把它翻译成“功”)。

科里奥利在比较了人,马,以及蒸汽机所能做的功后,建议用1000千克·米(他这里的千克实际上表示1千克物体的重力)作为衡量“功”的单位。

科里奥利建议的功的单位没有流行开。不过,“功”从此成为物理学中的专业名词。过去称呼“力与距离乘积”的那些复杂含混的词语,从此都消失了(或者用来表示其它物理量)。

在科里奥利37岁的著作中,人们看到另一个词,“动能”。科里奥利用这个词表示物体质量与速度平方的乘积的一半(高中物理内容)。在他之前,科学家们早已重视物体质量与速度平方的乘积。科里奥利发现,实际上,更值得关注的是这个量的一半。他一指出这一点,物理学家们立刻看出“果然如此”。大家很快采纳了“动能”一词以及科里奥利对动能的定义。(后来,英国物理学家兰金(William John Macquorn Rankine)提出了“势能”概念以及名称。我们就不讲他的故事了。)

科里奥利的最大成就,是发现了后世所称的“科里奥利力”。这是一种虚拟的力,超过了初中物理的范围。这里只指出,科里奥利也是从对机器运动的研究,做出这个发现的。这个发现能够解释许多事情,比如,当空气流(风)、河流与海洋中的水流,从赤道向北流动时,会向东拐弯;而当它们从北半球向赤道流动时,会向西拐弯。

我把我以前的一些文章,整理成了四本PDF电子书,有需求的读者可以点击下面链接购买(可查看各书目录试读):

4本启发思考的电子书:《给初学者讲物理》《思考的化学》《物理教科书名著品读》《教育·思维》

最新文章

随机文章

基本 文件 流程 错误 SQL 调试
  1. 请求信息 : 2026-04-04 21:14:17 HTTP/2.0 GET : https://c.sjds.net/a/461411.html
  2. 运行时间 : 0.158211s [ 吞吐率:6.32req/s ] 内存消耗:4,321.37kb 文件加载:140
  3. 缓存信息 : 0 reads,0 writes
  4. 会话信息 : SESSION_ID=f8ec5989761bfbfd5e201116ef143907
  1. /yingpanguazai/ssd/ssd1/www/c.sjds.net/public/index.php ( 0.79 KB )
  2. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/autoload.php ( 0.17 KB )
  3. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/composer/autoload_real.php ( 2.49 KB )
  4. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/composer/platform_check.php ( 0.90 KB )
  5. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/composer/ClassLoader.php ( 14.03 KB )
  6. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/composer/autoload_static.php ( 4.90 KB )
  7. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-helper/src/helper.php ( 8.34 KB )
  8. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-validate/src/helper.php ( 2.19 KB )
  9. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/helper.php ( 1.47 KB )
  10. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
  11. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
  12. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-container/src/Facade.php ( 2.71 KB )
  13. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/symfony/deprecation-contracts/function.php ( 0.99 KB )
  14. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/symfony/polyfill-mbstring/bootstrap.php ( 8.26 KB )
  15. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/symfony/polyfill-mbstring/bootstrap80.php ( 9.78 KB )
  16. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/symfony/var-dumper/Resources/functions/dump.php ( 1.49 KB )
  17. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-dumper/src/helper.php ( 0.18 KB )
  18. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/symfony/var-dumper/VarDumper.php ( 4.30 KB )
  19. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/App.php ( 15.30 KB )
  20. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-container/src/Container.php ( 15.76 KB )
  21. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
  22. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/provider.php ( 0.19 KB )
  23. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Http.php ( 6.04 KB )
  24. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-helper/src/helper/Str.php ( 7.29 KB )
  25. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Env.php ( 4.68 KB )
  26. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/common.php ( 0.03 KB )
  27. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/helper.php ( 18.78 KB )
  28. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Config.php ( 5.54 KB )
  29. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/app.php ( 0.95 KB )
  30. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/cache.php ( 0.78 KB )
  31. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/console.php ( 0.23 KB )
  32. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/cookie.php ( 0.56 KB )
  33. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/database.php ( 2.48 KB )
  34. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
  35. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/filesystem.php ( 0.61 KB )
  36. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/lang.php ( 0.91 KB )
  37. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/log.php ( 1.35 KB )
  38. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/middleware.php ( 0.19 KB )
  39. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/route.php ( 1.89 KB )
  40. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/session.php ( 0.57 KB )
  41. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/trace.php ( 0.34 KB )
  42. /yingpanguazai/ssd/ssd1/www/c.sjds.net/config/view.php ( 0.82 KB )
  43. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/event.php ( 0.25 KB )
  44. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Event.php ( 7.67 KB )
  45. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/service.php ( 0.13 KB )
  46. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/AppService.php ( 0.26 KB )
  47. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Service.php ( 1.64 KB )
  48. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Lang.php ( 7.35 KB )
  49. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/lang/zh-cn.php ( 13.70 KB )
  50. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/initializer/Error.php ( 3.31 KB )
  51. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
  52. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/services.php ( 0.14 KB )
  53. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
  54. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
  55. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/service/ModelService.php ( 2.04 KB )
  56. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
  57. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Middleware.php ( 6.72 KB )
  58. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
  59. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/Paginator.php ( 11.86 KB )
  60. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-validate/src/Validate.php ( 63.20 KB )
  61. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/Model.php ( 23.55 KB )
  62. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 21.05 KB )
  63. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/concern/AutoWriteData.php ( 4.21 KB )
  64. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 6.44 KB )
  65. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/concern/DbConnect.php ( 5.16 KB )
  66. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.33 KB )
  67. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 28.29 KB )
  68. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
  69. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
  70. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/model/contract/Modelable.php ( 0.09 KB )
  71. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Db.php ( 2.88 KB )
  72. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/DbManager.php ( 8.52 KB )
  73. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Log.php ( 6.28 KB )
  74. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Manager.php ( 3.92 KB )
  75. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/psr/log/src/LoggerTrait.php ( 2.69 KB )
  76. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/psr/log/src/LoggerInterface.php ( 2.71 KB )
  77. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Cache.php ( 4.92 KB )
  78. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/psr/simple-cache/src/CacheInterface.php ( 4.71 KB )
  79. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-helper/src/helper/Arr.php ( 16.63 KB )
  80. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/cache/driver/File.php ( 7.84 KB )
  81. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/cache/Driver.php ( 9.03 KB )
  82. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 1.99 KB )
  83. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/Request.php ( 0.09 KB )
  84. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Request.php ( 55.78 KB )
  85. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/middleware.php ( 0.25 KB )
  86. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
  87. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-trace/src/TraceDebug.php ( 3.40 KB )
  88. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/middleware/SessionInit.php ( 1.94 KB )
  89. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Session.php ( 1.80 KB )
  90. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/session/driver/File.php ( 6.27 KB )
  91. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/contract/SessionHandlerInterface.php ( 0.87 KB )
  92. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/session/Store.php ( 7.12 KB )
  93. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Route.php ( 23.73 KB )
  94. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/RuleName.php ( 5.75 KB )
  95. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/Domain.php ( 2.53 KB )
  96. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/RuleGroup.php ( 22.43 KB )
  97. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/Rule.php ( 26.95 KB )
  98. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/RuleItem.php ( 9.78 KB )
  99. /yingpanguazai/ssd/ssd1/www/c.sjds.net/route/app.php ( 1.72 KB )
  100. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/facade/Route.php ( 4.70 KB )
  101. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 4.74 KB )
  102. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/route/Dispatch.php ( 10.44 KB )
  103. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/controller/Index.php ( 4.81 KB )
  104. /yingpanguazai/ssd/ssd1/www/c.sjds.net/app/BaseController.php ( 2.05 KB )
  105. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/facade/Db.php ( 0.93 KB )
  106. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 5.44 KB )
  107. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/PDOConnection.php ( 52.47 KB )
  108. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/Connection.php ( 8.39 KB )
  109. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.57 KB )
  110. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 16.58 KB )
  111. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/Builder.php ( 24.06 KB )
  112. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/BaseBuilder.php ( 27.50 KB )
  113. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/Query.php ( 15.71 KB )
  114. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/BaseQuery.php ( 45.13 KB )
  115. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.43 KB )
  116. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
  117. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 20.07 KB )
  118. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.66 KB )
  119. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 7.01 KB )
  120. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 19.37 KB )
  121. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 7.11 KB )
  122. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.63 KB )
  123. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.77 KB )
  124. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/log/driver/File.php ( 5.96 KB )
  125. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
  126. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/log/Channel.php ( 3.89 KB )
  127. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/event/LogRecord.php ( 1.02 KB )
  128. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-helper/src/Collection.php ( 16.47 KB )
  129. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/facade/View.php ( 1.70 KB )
  130. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/View.php ( 4.39 KB )
  131. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Response.php ( 8.81 KB )
  132. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/response/View.php ( 3.29 KB )
  133. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/Cookie.php ( 6.06 KB )
  134. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-view/src/Think.php ( 8.38 KB )
  135. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/framework/src/think/contract/TemplateHandlerInterface.php ( 1.60 KB )
  136. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-template/src/Template.php ( 46.61 KB )
  137. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-template/src/template/driver/File.php ( 2.41 KB )
  138. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-template/src/template/contract/DriverInterface.php ( 0.86 KB )
  139. /yingpanguazai/ssd/ssd1/www/c.sjds.net/runtime/temp/4b635f01740da80a68ecf76597ee81b6.php ( 12.06 KB )
  140. /yingpanguazai/ssd/ssd1/www/c.sjds.net/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000960s ] mysql:host=127.0.0.1;port=3306;dbname=c_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.001463s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000661s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000590s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.001118s ]
  6. SELECT * FROM `set` [ RunTime:0.000521s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.001309s ]
  8. SELECT * FROM `article` WHERE `id` = 461411 LIMIT 1 [ RunTime:0.002312s ]
  9. UPDATE `article` SET `lasttime` = 1775308457 WHERE `id` = 461411 [ RunTime:0.001564s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000585s ]
  11. SELECT * FROM `article` WHERE `id` < 461411 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000990s ]
  12. SELECT * FROM `article` WHERE `id` > 461411 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.001298s ]
  13. SELECT * FROM `article` WHERE `id` < 461411 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.002542s ]
  14. SELECT * FROM `article` WHERE `id` < 461411 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.003503s ]
  15. SELECT * FROM `article` WHERE `id` < 461411 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.004757s ]
0.159812s