- A review paper on geometric methods in control theory for mechanical
systems

**Reference:***The bountiful intersection of differential geometry, geometric mechanics, and geometric control theory* - Low-order controllability is connected with simple motion planning
algorithms

**Reference:***Low-order controllability and kinematic reductions for affine connection control systems* - The mechanical meaning of ``linearly controllable''

**Reference:***The linearisation of a simple mechanical control system* - Basic discussion of controllability for ``simple mechanical control
systems.'' This work gives the necessary and sufficient conditions for
local configuration accessibility, and some too strong sufficient conditions
for local configuration controllability

**Reference:***Configuration controllability of simple mechanical systems* - Generalisation to systems with constraints of previous work

**Reference:***Simple mechanical control systems with constraints* - Single-input affine connection control systems are uncontrollable

**Reference:***Local configuration controllability for a class of mechanical systems with a single input* - A discussion of the relationship between motion planning and low-order
local controllability for affine connection control systems

**Reference:***Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples* - An explicit motion planning algorithm for the snakeboard

**Reference:***Kinematic controllability and motion planning for the snakeboard* - Some motion control primitives for systems on Lie groups with certain
controllability properties

**Reference:***Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups* - An investigation of force and time-optimal control for a planar rigid
body

**Reference:***Optimal control for a simplified hovercraft model* - Basics of time-optimal control for affine connection control systems,
and an application to the robotic leg and the planar rigid body

**Reference:***Time-optimal control of two simple mechanical systems with three degrees of freedom and two inputs* - The derivation of the ``adjoint Jacobi equation'' from the Pontryagin
maximum principle for affine connection control systems. The setting in
this paper is quite general

**Reference:***The geometry of the maximum principle for affine connection control systems* - Integrability conditions for joint partial differential equations of
kinetic and potential energy shaping

**Reference:***A geometric framework for stabilization by energy shaping: Sufficient conditions for existence of solutions* - Integrability conditions for the partial differential equations of
potential energy shaping

**Reference:***Potential energy shaping after kinetic energy shaping* - Formulation of the energy shaping partial differential equations using
differential and affine differential geometry

**Reference:***Notes on energy shaping*