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Part III ›
Rigid Bodies and Rotating Frames
Rigid Bodies and Rotating Frames
foundations results +17 more equations +9 more phenomena depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) step_from (declared) step_from (declared) depends_on (declared) depends_on (declared) definition 29.1: Rigid body 29.1 Rigid body definition 29.4: Angular velocity 29.4 Angular velocity notation 29.9: The z–x–z Euler angles used in this treatise 29.9 The z–x–z Euler… definition 29.13: Inertia tensor, continuum form 29.13 Inertia tensor,… definition 29.18: Classification of tops 29.18 Classification o… definition 29.19: Inertia ellipsoid 29.19 Inertia ellipsoid definition 29.35: The Lagrange top 29.35 The Lagrange top proposition 29.2: Six degrees of freedom 29.2 Six degrees of f… theorem 29.3: Euler's rotation theorem 29.3 Euler's rotation… proposition 29.5: The velocity field of a rigid body 29.5 The velocity fie… proposition 29.6: The angular velocity does not depend on the base
point 29.6 The angular velo… theorem 29.7: Transport theorem 29.7 Transport theorem proposition 29.8: Chasles: the general displacement is a screw 29.8 Chasles: the gen… proposition 29.11: Angular velocity in Euler angles 29.11 Angular velocity… proposition 29.14: Angular momentum and kinetic energy 29.14 Angular momentum… proposition 29.15: Positivity 29.15 Positivity theorem 29.16: Principal axes 29.16 Principal axes proposition 29.17: Triangle inequalities 29.17 Triangle inequal… theorem 29.20: Parallel-axis theorem 29.20 Parallel-axis th… corollary 29.21: The centre of mass minimizes the moment 29.21 The centre of ma… equation 29.1: eq:rigid-constraint eq. (29.1) equation 29.4: eq:rigid-transport eq. (29.4) equation 29.11: eq:rigid-angular-momentum eq. (29.11) equation 29.12: eq:rigid-kinetic-energy eq. (29.12) equation 29.21: eq:rigid-euler-vector eq. (29.21) equation 29.31: eq:rigid-chandler-love eq. (29.31) equation 29.32: eq:rigid-chandler-liouville eq. (29.32) equation 29.33: eq:rigid-chandler-rate eq. (29.33) equation 29.35: eq:rigid-top-lagrangian eq. (29.35) equation 29.43: eq:rigid-nutation-amplitude eq. (29.43) equation 29.45: eq:rigid-steady-precession eq. (29.45) equation 29.52: eq:rigid-kovalevskaya-eta eq. (29.52) equation 29.51: eq:rigid-kovalevskaya-zeta eq. (29.51) phenomenon 29.31: The intermediate-axis instability 29.31 The intermediate… phenomenon 29.34: Free nutation of the Earth 29.34 Free nutation of… phenomenon 29.38: Nutation of a released top 29.38 Nutation of a re… phenomenon 29.46: A fast spinning top does not fall 29.46 A fast spinning… phenomenon 29.49: Precession of the equinoxes 29.49 Precession of th… phenomenon 29.53: Rotation is locally detectable, uniform motion is
not 29.53 Rotation is loca… phenomenon 29.55: Effective gravity varies with latitude 29.55 Effective gravit… phenomenon 29.56: Falling bodies are deflected eastward 29.56 Falling bodies a… phenomenon 29.58: Weather systems circulate, and the sense is set by
the hemisphere 29.58 Weather systems… phenomenon 29.61: The Foucault pendulum 29.61 The Foucault pen… The chain of Rigid Bodies and Rotating Frames: 43 of 69 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.