Certain aspects and features relate to a system that includes a drilling tool, a processor, and a non-transitory memory device that includes instructions that are executable by the processor to cause the processor to perform operations. The operations include receiving input data that corresponds to characteristics of at least one of drilling fluid, a drillstring, or a wellbore. The operations also include calculating at least one dynamic sideforce and at least one dynamic, hydraulic force based at least in part on the input data. The operations also include determining an equilibrium solution for an output value using the at least one dynamic sideforce and at least one dynamic, hydraulic force. The operations also include applying the output value to the drilling tool for controlling operation of the drilling tool.