definition 19.31 Energy
open in the book ·
parts/03-classical-mechanics/02-newtonian-dynamics.tex:851
· p. 743
- ground object -- no derivation owed
Rests on
-
depends_on
definition 19.30
Conservative force and potential energy
¶
- depends_on equation 19.2 eq:newt-second-law ¶
-
depends_on
postulate 19.8
Newton's second law
¶
-
depends_on
definition 19.5
Linear momentum
¶
-
depends_on
definition 18.10
Velocity
¶
- depends_on definition 7.26 Derivative of a function at a point ¶
- depends_on definition 18.9 Position ¶
- depends_on definition 13.9 Tangent vector to a curve ¶
- depends_on definition 19.3 Mass ¶
-
depends_on
definition 18.10
Velocity
¶
-
depends_on
postulate 19.6
Newton's first law
¶
-
depends_on
definition 18.8
Inertial frame of reference
¶
- depends_on definition 18.7 Frame of reference ¶
- depends_on definition 18.6 Free particle ¶
- depends_on definition 19.5 Linear momentum ¶ ↺
-
depends_on
definition 18.8
Inertial frame of reference
¶
-
depends_on
definition 19.5
Linear momentum
¶
- depends_on definition 19.29 Kinetic energy ¶
Supports
- depends_on proposition 27.20 Conservation of energy ¶
-
depends_on
theorem 19.32
Conservation of energy
¶
- depends_on phenomenon 50.6 No material surface ¶
- depends_on phenomenon 19.33 Mechanical energy is conserved ¶
-
depends_on
theorem 21.43
Conservation of energy
¶
-
depends_on
proposition 29.36
Three first integrals
¶
- depends_on phenomenon 29.38 Nutation of a released top ¶
-
depends_on
proposition 29.43
The three integrable heavy tops
¶
- depends_on remark 29.45 What integrability buys, and where it stops ¶
- depends_on remark 29.44 The Kovalevskaya integral ¶
- depends_on proposition 29.40 The sleeping top ¶
-
depends_on
theorem 29.37
Reduction to one degree of freedom
¶
- depends_on phenomenon 29.38 Nutation of a released top ¶ ↺
- depends_on proposition 29.40 The sleeping top ¶ ↺
- depends_on remark 29.42 The closed form, and the mathematics it needs ¶
- depends_on theorem 27.10 Lagrange–Dirichlet ¶
-
depends_on
proposition 29.36
Three first integrals
¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Conservative force and potential energy | declared | parts/03-classical-mechanics/02-newtonian-dynamics.tex:857 |
depends_on |
→ | Kinetic energy | declared | parts/03-classical-mechanics/02-newtonian-dynamics.tex:857 |
depends_on |
← | Conservation of energy | declared | parts/03-classical-mechanics/10-central-forces-statics.tex:600 |
depends_on |
← | Conservation of energy | declared | parts/03-classical-mechanics/02-newtonian-dynamics.tex:887 |