Dealing with a similar issue, I encountered an error while attempting to include the TrackBallControls typescript file in my project:

THREE.TrackballControls is not a constructor

I realized that my three.d.ts file did not have a declaration for THREE.TrackballControls, so I appended my TrackBallControls at the end of the file with the "export" keyword, like this:

export class TrackballControls extends EventDispatcher {
    constructor(object: Camera, domElement?: HTMLElement);

    object: Camera;
    domElement: HTMLElement;

    // API (omitted for brevity)
    
}

I also included a new javascript file in my project with THREE.TrackballControls, which I found here.

Subsequently, I faced a TypeError related to my update function.

this.controls.addEventListener('change', this.render); 

Ultimately, I resolved it by commenting out the above line and retaining the following:

this.controls.update();

Since then, everything is functioning smoothly.

Provided below is a solution that serves as a partial answer and workaround instead of an "official" response. It is hoped that this will be beneficial to others.

To summarize:

In the webpack.config.js file, define THREE as an external module:

externals: {
  three: 'THREE'
},

This prevents THREE from being included in the bundle.js, which has its advantages and disadvantages. Overall, it is a positive outcome.

Concluding HTML script tags:

...
<script src="http://threejs.org/build/three.min.js"></script>
<script src="http://threejs.org/examples/js/controls/OrbitControls.js"></script>
<script src="bundle.js"></script>
</body>
</html>

It should be noted that "external" does not imply "must originate from a third-party site". Rather, it signifies "not included in bundle.js".

More Detailed Explanation

I had been attempting to address numerous issues simultaneously. I had come to a realization similar to this:

"WebPack can gather all dependencies, such as THREE and trackball modules along with other THREE utility modules, incorporate them with typings information, package, compress, and bundle them into a single bundle.js file - so might as well do everything."

While this statement holds true, it is not the most efficient method to proceed.

Instead, I adopted the viewpoint that WebPack can neatly package the application code, and while it can package the vendor code too, doing so leads to various peculiar issues for limited benefit - thus, keeping those dependencies external is preferred.

In my attempts to include both THREE and trackball controls within the bundle.js, I encountered significant challenges. Integrating THREE itself was relatively straightforward and successful on the initial attempt, but incorporating the trackball or orbit controls presented perplexing obstacles.

There were multiple hurdles to overcome.

One issue stemmed from inaccurately named typing information for dt:

$ ls -C1 typings/globals/
three
three-orbitcontrols
three-trackballcontrols

These names are intuitive and sensible - however, the NPM modules differ:

$ grep -i three package.json
"three": "^0.77.1",
"three-orbit-controls": "^72.0.0",
"three.trackball": "0.0.1"

While uncertain, it appears that these naming disparities cause webpack difficulties in identifying which modules to include in the bundle based on imports.

Even after successfully importing, resolving the name THREE.OrbitControls proved elusive. The NPM module for the OrbitControls exports a function for invocation, requiring the existing THREE module as an argument before incorporating the OrbitControls. Despite this, the webpack initialization code lacks knowledge on how to execute this function, leaving me at a loss for resolution.

The following code snippet would result in compilation errors yet generate functional JS code:

import OrbitControls = require('three-orbitcontrols');
THREE.OrbitControls = OrbitControls(THREE);  // compile error but still emits JS that works

This approach demanded excessive effort for a simple concept: renaming directories, tweaking startup code, overlooking compile-time errors...

It gradually became apparent that there is no pressing need for THREE to be contained within the bundle, nor does it matter if the OrbitControls possess types or not. In fact, having a smaller bundle equates to improved speed and efficiency.

How can THREE be removed from the bundle? Simply declare it as external. Subsequently, the default NPM and typings modules operate seamlessly. Furthermore, the necessity of typings modules for the orbit or trackball controls remains uncertain.

Having tried the steps mentioned above without success, which included:

"three": "^0.84.0",
"@types/three": "^0.83.0",
"three-js": ">=79.0.0",
"three-trackballcontrols": "0.0.5",
"webpack": "^1.14.0"

I proceeded to take the following actions:

npm install save-dev three-trackballcontrols
mkdir node_modules/@types/three-trackballcontrols
cd node_modules/@types/three-trackballcontrols
cp ../three/three-trackballcontrols.d.ts ./index.d.ts

Subsequently, within index.d.ts, I modified

class TrackballControls extends EventDispatcher {...}

to

export class TrackballControls extends EventDispatcher {...}

.

Afterward, at the end of index.d.ts, I appended

declare module "three-trackballcontrols" {
  export = THREE.TrackballControls;
}

Then, moving on to the three typings section, I navigated to cd ../three and in index.d.ts, I changed

/// <reference path="three-trackballcontrols.d.ts" />

into a commented line

/* <reference path="three-trackballcontrols.d.ts" /> */

Lastly, in the renderer code, I utilized

import TrackballControls = require('three-trackballcontrols');

and initiated

controls = new TrackballControls(camera);

instead of

controls = new THREE.TrackballControls(camera);

I encountered a frustrating issue:

ERROR TypeError: WEBPACK_IMPORTED_MODULE_1_three.TrackballControls is not functioning as a constructor

This error surfaced after upgrading my project to angular-cli version 4.0. Sharing my code in hopes of aiding others.

Here's an excerpt from my package.json file:

"dependencies": {
    ...
    "three": "^0.82.1",
    "three-trackballcontrols": "0.0.5",
    ...
  },
"devDependencies": {
    ...
    "@types/three": "0.81.0",
    ...
  }

Within my Component.ts file:

...
import * as THREE from 'three';
import TrackballControls from "three-trackballcontrols";
...
this.webGLRenderer = new THREE.WebGLRenderer({antialias: true});
this.camera        = new THREE.PerspectiveCamera(
            this.view_angle,
            this.width / this.height,
            this.near,
            this.far
        );
...
this.controls = new TrackballControls(this.camera, this.webGLRenderer.domElement);

When working with Angular CLI (Angular 4), I encountered the same issue:

ERROR TypeError: __WEBPACK_IMPORTED_MODULE_1_three_trackballcontrols__.TrackballControls is not a constructor

Following mok's advice, I was able to resolve the error and get the code functioning properly.

One observation I made was that importing TrackballControls using the following syntax resulted in an error:

import { TrackballControls } from 'three-trackballcontrols';

A successful import should follow the method outlined by mok:

import TrackballControls from 'three-trackballcontrols';