proposition 21.56 The two prescriptions and their difference

Rests on

• depends_on definition 21.55 Vakonomic prescription ¶
  • depends_on equation 21.53 eq:lag-hamilton ¶
  • depends_on equation 21.55 eq:lag-pfaffian ¶
• depends_on equation 21.57 eq:lag-nonholonomic-eom ¶
• depends_on theorem 16.41 Multiplier rule for pointwise constraints ¶
  • depends_on equation 16.37 eq:calcvar-pointwise-constraints ¶
  • depends_on lemma 16.18 Fundamental lemma ¶
    • depends_on definition 16.15 Variation; the first variation ¶
      • depends_on definition 16.11 Admissible class; functional ¶
        • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on theorem 7.40 Continuous functions are integrable ¶
      • depends_on equation 7.177 eq:ana-functional-derivative ¶
    • depends_on theorem 7.40 Continuous functions are integrable ¶ ↺
    • proves proof ch:14-calculus-of-variations@proof-8 ¶
  • depends_on theorem 16.35 System of Euler–Lagrange equations ¶
    • depends_on lemma 16.20 Mixed form ¶
      • depends_on corollary 7.44 Substitution and integration by parts ¶
        • depends_on proposition 7.31 Chain rule ¶
        • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • proves proof ch:05-real-analysis@proof-26 ¶
      • depends_on lemma 16.19 du Bois-Reymond ¶
        • depends_on equation 16.18 eq:calcvar-dbr-hyp ¶
        • depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
        • proves proof ch:14-calculus-of-variations@proof-9 ¶
      • proves proof ch:14-calculus-of-variations@proof-10 ¶
    • depends_on theorem 16.22 Euler–Lagrange ¶
      • depends_on equation 16.15 eq:calcvar-first-variation ¶
      • depends_on lemma 16.20 Mixed form ¶ ↺
      • depends_on proposition 16.16 Stationarity is necessary ¶
        • depends_on definition 16.15 Variation; the first variation ¶ ↺
        • depends_on definition 16.13 Weak and strong extrema ¶
        • depends_on lemma 7.33 Fermat: interior extremum ¶
        • proves proof ch:14-calculus-of-variations@proof-6 ¶
      • proves proof ch:14-calculus-of-variations@proof-11 ¶
    • proves proof ch:14-calculus-of-variations@proof-19 ¶
  • proves proof ch:14-calculus-of-variations@proof-23 ¶
• proves proof ch:04-lagrangian-mechanics@proof-14 ¶

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